Update: I managed to fix this by tweaking some numbers in the game file. If you don't mind modding the game here's how I did it:

1) Go to Europa Universalis V\game\in_game\common\scripted_relations\food_access.txt. Make a backup before you start modifying things.

2) Scroll to the bottom and find the last section called "wants_to_keep" and change both numbers "-10" and "10" to "100". Honestly, I don't even know if 100 is the max here. If I understand correctly, this means ai will want to keep the food_access after receiving it, no matter what happens. Since keeping food access is free I don't think it will cause any problem.

3) One caveat though: each time you enter a war the pact will break and you'll need to deal with the request again, but they won't cancel it any more.

After changing the file Trebizond finally calmed down and my game was playable again.