I think Pressac has offered the best explanation for the exaggerated figures (death toll and cremation capacity): they were passed on to him by his guides in Auschwitz-Birkenau.
I do not see why Hoess or whoever guided Franke-Gricksch around Birkenau would have given him such outrageously exaggerated figures. After all, Himmler had been highly critical of the dodgy statistics being fed to him, which is why he employed Korherr to write his famous report.
By the time Franke-Gricksch visited Birkenau in May 1943, Korherr's report had been handed in, and everybody in the SS must have been aware that Himmler demanded accuracy. There would have been nothing to gain by giving Franke-Gricksch figures that were so obviously false.
Furthermore, Hoess testified post-war that he was instructed not to keep a record of the numbers exterminated. No figure was supposed to exist. Therefore I think it hardly likely that Franke-Gricksch would have asked for a figure of numbers exterminated, or have been given one, or that he would have included a figure in a report.
Where do you know that Höß gave him the figures? Where do you know that Franke-Gricksch wrote a report for people in Berlin who could check the true figure? Where do you know that his guide in Auschwitz knew that Franke-Gricksch was writing a report for people in Berlin who could check the true figure? Where do you know that they knew that Franke-Gricksch was writing a report?
If you or anyone else has reliable information on the background to Franke-Gricksch's report, why he went to Auschwitz, who he was reporting to, what the purpose of his report was. etc, I would be very interested to see it. I might even revise my opinion.
We've already gone through this, Michael. There was in fact a spur line leading into Birkenau just behind crematorium II, which Franke-Gricksch presumably visited in 1943. He saw this spur line and he concluded that the Jews were directly shipped infront of the crematorium's back-entrance. (note the homicidal gas chamber and the little chimnies, through which the poison gas was thrown into the gas-chambers, in the background)
The track shown in the picture is apparently a temporary one laid for transporting construction materials. It appears to be a narrow-gauge light track, and could not have been connected to the main railway running past Birkenau camp. I do not think that anyone who saw that track (it it was still there in May 1943; it does not appear on maps of the camp) could have assumed that it could have carried full-sized trains on which Jews arrived.
What I think is certain is that there is not a shred of evidence or hint that this document was manipulated. It is of course possible that the last two lines about the death toll and cremation capacity were simply added after the war, but I see absolutely no reason why the investigators for the Nuremberg trials should have done this, after all the report was never introduced as evidence nor would the exaggerated figures have helped the prosecution.
I think you are quite right that this document would not have helped the prosecution at the Nuremberg trials. That may well be the reason why it was never introduced as evidence; the prosecutors probably looked at it and concluded that it was "too good to be true". It seems to have been filed away, only to be discovered years later by undiscriminating historians.
It is possible that an original report, which surely would have observed the discretion about killings of non-working prisoners that is typical of the correspondence of the Auschwitz administration, was "massaged" by an over-enthusiastic investigator in order to turn it into something that said explicitly what was being heard from survivor witnesses.