I'm glad you've got your answer. Although, it seems to be an answer to a question that you haven't actually asked. Never mind.
The invasion plan proposed by Graziani (talking history now not fiction) was rejected by Cavagnari at the Chiefs of Staff meeting on 5 June 1940. Rejected primarily because of the recognition that the army had not as yet trained any troops for an opposed amphibious landing, the navy had no specialized amphibious landing craft and the airforce was deployed for an operation against Yugoslavia.
Having rejected the 'army plan' to land 40,000, the navy were asked to come up with an alternative which they produced on 18 June 1940. This involved just 20,000 but came with several caveats and also suggested that there seemed little point in doing it as the British had already removed the Fleet from Malta and thus removed the 'threat'. Why not just contain Malta by sea and air power? It was largely based upon this analysis that the proposed invasion was kicked into touch.
In history, it wasn't Mussolini's "stupidity" that called a halt to the invasion planning, it was the Italian Navy's pessimism that it was doable or even necessary.
Moreover, was 28 August 1940 a realistic D-Day when, even as late 18 June, NOTHING practical had begun? Still no training of the landing forces, still no conversion work begun on shipping. Is 2 months sufficient time?
Had the Italians ever decided to go ahead and start practical preparations, they would have taken some time. I suspect these would have become known to the British who would have altered their strategic outlook and dispositions. Moreover, an invasion of Italy is almost certain to have had a knock-on effect of some description to Italian plans to invade Egypt and Greece.