Does anyone have an idea how quickly production could be transitioned from the VK3601 to the Panther?
If you assume that all German mains tank factories had converted to VK36.01 by mid 43, then you have MAN, DB, MNH, Demag, Henschel Alkett, Krupp, etc all producing it. starting with MAN, the parent company, and to minimise production disruption, you would probably switch one main factory at a time. You could be producing only Panthers by early 44 with minimal loss of volume.
By that time (mid 43) the VK36.01 would probably be using the engine and gearbox intended for the Panther anyway.
OTL Henschel stopped producing PzIII in July42 and delivered the first production Tiger I that same month, so each factory you convert will probably cost you less than a month of its production.
But remember I'm a rifleman, not an engineer. I might be prone to oversimplifying.
Regarding production volume, here are the figures for 1941, medium tanks only:
Germany, 1673 PzIII, 467 PzIV. With 540 StuG you get 2680 AFV. It looks good until you see that GB had built, in the same year:
762 Covenanter, 655 Crusader, 1038 Matilda, 1621 Valentine and 690 Churchill, for a total of 4766 AFV. And it was Germany who was fighting the USSR...
Simply put, there are some 3000 tanks missing in Germany 41 production plans, and the lack of them made, among other factors, their goals in the USSR unattainable.