Allow me to expand the universe of possibilities under the heading of "Slightly Stronger Barbarossa Forces."
My initial treatment specifies 20 extra divisions but honestly if those divisions existed the outcome is clear to me - and sufficiently clear as to be less interesting than I initially thought.
I've also been mulling a smaller initial force delta combined with the already-described strategic conception of Barbarossa as at least a 2-year campaign.
Under this scenario, I believe an extra 8 mechanized divisions would have given Germany a good chance of winning the war. Let me explain:
In Army Group Center, the difference between the successful June-July campaign and a failed campaign is Hoth's Panzergruppe with 7 divisions. Absent these 7 divisions, Guderian's penetrations would have lacked a second pincer to envelop Western Front even had he achieved similar operational depth (doubtful given that some of anti-Hoth RKKA would have faced Guderian). AGC can probably still pinch off the absurdly-positioned forces in the Bialystok salient but after that Western Front probably retreats to Smolensk having lost ~500k fewer prisoners and their equipment. That ATL means likely no Kiev encirclement (Bock barely held his front in August and another 500k Soviets would have at least required Guderian to stick around and help).
With 8 divisions, Rundstedt could have had a second panzer-pincer throughout the Ukraine campaign. 8 divisions are probably insufficient to launch the grand encirclement from Romania that my 20div-ATL involves. And AGS's front is less conducive to a Bialystok/Minsk-type operation than AGC's. But such as an operation isn't necessary, IMO. If, for example, Rundstedt encircles "only" most of 5th and 6th armies in the border battles - with a shallower swipe largely west and southwest of the Pripyat marshes - then he could remove ~1/3 of Kirponos' force by early July. Now fast forward to mid-July and the move from Western Ukraine to the Dniepr. Here's a couple images of that campaign OTL for reference:
As can be seen - as many of you know - AGS broke into operational freedom through Zhitomir around the third week of July and then executed a single envelopment of 6th and 12th armies around Uman, linking up with infantry forces. The encirclement took a very long time to enact and the Soviets probably could have escaped it given a reasonable withdrawal timeline. It bagged "only" ~100k prisoners because the surrounded formations fought their pursuers for a very long time before the ring closed.
If Rundstedt had another Panzergruppe, this stage of the battle would have (1) faced weaker opposition due to border battle encirclement and (2) could have been a quicker, bigger, cleaner double envelopment along the lines of what Bock was doing simultaneously in the center.
Re (2), AGS could thrown its spearheads north and south of Zhitomir instead of through it - say through Korosten and Kazatin. EVERY TIME the Germans used double-enveloping panzer armies in 1941 they succeeded: The RKKA didn't stop a panzer army's penetration until November, C&C was insufficient to recognize the enirclement danger until too late, and Stalin/STAVKA wouldn't permit withdrawals in a timely fashion. It seems obvious to me that AGS would have completed at least a couple Minsk-scale Kessels given another Panzergruppe.
After the Kessels in June/July, additional encirclements would likely have happened in the Dniepr bend, such as a better version of the partially-successful OTL encirclement at Nikolayev. The OTL Germans had only one panzer division - 16th - to cut off the city and from what I've read captured "only" ~60k prisoners (anyone have good sources on this battle? There's decent background in this old thread: viewtopic.php?t=145794
Critically, AGS would have the means to encircle Kiev without Guderian/Bock's help. And ATL the Kiev Kessel would have likely happened sooner because AGS reaches the Dniepr quicker than OTL.
Some implications for the wider campaign:
With Southwest and Southern Fronts having lost many more men (~500k delta) by August, Stalin is forced to reinforce Ukraine to a much greater extent than OTL (I assume that he would not abandon Kiev in August just as he refused to do so in September). That means Timoshenko has fewer men to launch at Bock during August. Bock is stronger on his eastern front because AGS will be covering his right flank on the Desna as it pushes forward to encircle Kiev during August. Unlike OTL, Bock would have strong mobile forces to counter Timoshenko's attacks on his front. AGC would probably encircle/destroy large portions of Timoshenko's weaker thrusts, resulting either in catastrophic Red losses or a truly quiet central sector during much of August as AGC waits for the rails and supplies before pushing on.
This gives the opportunity for an earlier Taifun. Hitler/OKH would face a strategic dilemma similar to, but better than, the OTL dilemma of late summer: reinforce the drive on Moscow with some of AGS's armor or go for broke in the South, aiming to reach the Don and cross its southern course into the North Caucasus. IMO the southern option is far wiser as it gets you Maikop and Grozny during early '42 and at least shuts off Baku by the end of the year. A Hitler who is thinking in terms of a longer war would almost certainly choose that option, as he did in OTL '42. Leaving Moscow in Russian hands at the end of '41 forces Stalin to concentrate forces there, preventing counterattacks elsewhere and setting up an enormous Kessel for the '42 campaign.
That leaves AGC to execute Taifun without significant armor transfer from its flanks. But it's also facing weaker opposition, as Stalin has to do something to stop AGS in eastern Ukraine or at least before it reaches Stalingrad. Say AGC executes a Vyazma kessel instead of Vyazma-Briansk during late August and early September. It still has time for another Kesselschlacht before Rasputitsa so the Moscow Offensive casualty exchange is about the same. Lacking the "do or die" mission towards Moscow in November, AGC enters secure winter lines outside the city and meets Russian counterattacks from a position of strength.
Around Leningrad it's a similar story: greater losses in the Ukraine and a stronger AGS mean more forces sent south and fewer in the north. A Hitler committed to "Ukraine first, Leningrad second, Moscow third" should let Leeb keep all of Hoepner's Panzergruppe. With a couple more panzer divisions and facing weaker opposition, AGN can probably push through Tikhvin and join the Finns on the Svir, thereby sealing Leningrad. Whether the city lingers deep into the winter or falls quickly, the RKKA loses another ~500k men and the Ostheer frees up a score of divisions for other missions during '42 (taking Archangelsk, for example). Plus it's a morale coup.
In this version of the slightly stronger Barbarossa, Germany captures about a million more Reds in Ukraine and Leningrad during '41. More captured Reds means fewer dead Germans; at a 3-1 bloody casualty ratio that's ~300k fewer German losses.
Besides the operational implications of the 8 more divisions, the multi-year conceptions builds strategic benefits throughout the Barbarossa period. Germany mobilizes its manpower for war throughout '40-'41 as it did later in the war (as in original ATL sketch but at a slower pace). This would mean more and quicker replacement of losses at the front, having particularly great impact on German rifle strength during the first winter. It would mean timely provision of winter clothing. It could mean further additions of mobile divisions for the '42 campaign; it would at least mean full strength for all these divisions by May 42.
German planners would have responded more urgently to the T-34 threat than they did OTL- proposing to upgun the MkIV in July rather than beginning to study the issue in November. That means many more long-gunned MkIV's in '42 and, more crucially, more heavy Pak for the infantry. Germany doesn't cut artillery ammunition so low in '40-'41 that Ostheer has to radically economize during the winter. More StuG's are present at the beginning of Barbarossa and the supply increases significantly with time (this further cuts Ostheer losses during '41-42). The long war convinces German logistics and railway planners that more train engines will be needed, preventing or ameliorating the transport crisis of the first winter and its effects on the economy (this would have been obvious: supplying 3mil men deep into Russia would be impossible without robbing the economy of rail lift; it wasn't obvious because only a skeletal force was expected to remain in Russia by winter).
ATL May 1942 would see ~500k more Germans at the front and a Red Army with ~million fewer troops. RKKA could not launch a Uranus-like operation against the Ostheer's drive southward because Germany would launch another Moscow battle that summer (and if Stalin abandoned Moscow to defend the Caucasus, the flank of his attack on the Don/Volga flank would be exposed to AGC).
The 42 campaign would see the Germans take Moscow, the Caucasus, and much/most of the Don-Volga Russian heartland. With the Caucasus gone, Russia's resistance would be on borrowed time: either the US/UK find a way to ship millions of tons of oil or Russian agriculture and mobility collapse during 1943.
1943 would be interesting: Russia would still have a large army in the field, but not one capable of pushing back the Germans and it would be on borrowed time. Allies could maybe invade France to save Russia but that's extremely risky: Air supremacy isn't quite established in OTL 43; ATL Germany would have greater fuel and industrial resources at its disposal. Having lost many fewer men than OTL (no Stalingrad, more Russians captured rather than traded ~3-1 in shooting duels), and requiring fewer men to hold its Eastern Front, OKH can counter any Allied move into France with very powerful forces. Churchill had no appetite for a big land showdown with Germany; I doubt Roosevelt could have dragged him into one even had Roosevelt resolved to make the gamble.
Ok that's the revised sketch for now. I think this ATL sees some kind of armistice in the East and Hitler surviving the war. More to say...
The point of this exercise is to say that Germany doesn't really need 20 divisions to win - 8 might have been enough. Getting to 8 divisions is a lot easier than getting to 20, though I continue to believe that 20 was feasible. Mobilization for a multi-year Eastern campaign means Germany's forces get stronger throughout 41 and into 42, rather than entering the 42 campaign much weaker than in 41, only to rebound to maximal strength in 43 when it was way too late.