I have examined the saves and I see that the problem comes from requests from HQs to cities being too aggressive (too big) when compared what the HQs actually ask for later in the supply phase. It looks like the armies like to have 2-3 times the number of supplies that they really want. The problem is it's hard to nail the correct value, because city resupply is done before upgrades and replacements. Which means there has to be some extra included in case some units will get massive replacements (mostly due to TOE upgrade - especially a newly converted corps from brigades). That's why you start hitting such problem when the global supply stock is about 200-300% of the need (this % is calculated after the cities have been stocked). I think I can safely reduce this value from the 2x-3x range to 1.5x range and the supply system will continue to work with lower overall supply percentages. Of course the city supply system should be fixed to deal with shortages, but for now reducing the multiplier will help, unless someone will be really scraping the bottom of the barrel.
Anyway, I have noticed that you have some tank brigades (converted from Tank Divisions) that are attached to STAVKA but kept far away from it, who are thus unable to return extra stocks they have (besides they have low chances to pass any leader rolls: morale 50%, initiative 53.3%, admin 53.3%, mech 43.7% with a nominally 8/8/7/7 leader), so it's better to attach them to some other HQ or keep them closer to STAVKA.
Keep an eye on supply levels, as out of 108k total supply production 47k is used by factories, 14k by fort building and 41k is eaten by units (where some units do not eat at all). This means you are close to living from hand to mouth or worse, eating your remaining stocks.