I have the same problem. I have a kingdom above more than half of the map from Vladia, over Betannian and Sturgia, eliminated Southern and Western Empire and reached something about day 2800. To complete the main quest I just need to finish of the Nordern Empire with their last 4 citys and 7 castles. Then only Khuzait and Aserai will remain. But it is Impossible right now.
I don't use mods.
At first, to solve the issue I droped all of my food to eat the food of the other partys. At the beginning I thought this works, because the "Overburdened" drops to 0, but in the end it doesnt matter. They earning grain to fast. Like in one fight I looted 3000 grain and I make a lot of fights to finish of the empire. Every time I drop all the food but the AI keeps it all. I disband the army, because"Overburdened" has a score of -4.0 and take new partys but after one battle the whole problem starts again. Speed is reduced to 1.0.
The starving thing was one thing the player can prevent. Every time before I build an army I bought tons of food. Like up to 2000 grain. Of course the AI armys didnt do that, so after a while they began to reduce their numbers because of starvation.
Before, I really did not care about graphic issues or other bugs that can be evaded. I did not care about the stupid behavior of AI armys or other things. I really loved Bannerlord. Everything was fine.
But with this problem, in my opinion, this normally fantastic game become unplayable. Just because there is nothing the player can do anymore if there is an own kingdom that dependent on the armys, which are now just a slow, never reaching their destination joke of 2000 man on the map.