chapter4 is the hardest chapter. the best way to deal with the upkeep is:
on the first day that you get to alfheimr, get the first missions from all the captains and start working on completing them (after finishing borge's mission to get permission to travel in alfheimr ofc). 4 of the missions will lower the raid-upkeep, which is by how much the upkeep is raised each day. so its important to finish them on the 2nd or 3rd day in alfheimr.
every day collect menually all the food from all fields and the barn- this way you will also collect free tokens. you should donate all the tokens each day to one of the 3 depots to raise the reputation with the depots' factions and you also get 1 food for each token.
if you dont have a mission to fight (and dont want to fight for loot) donate to the fighters in the fields and depot. it will lower the upkeep by 1. fighting there or agains jotuns can lower the upkeep by 1 too, but even without that you should have enough food for about 15 days in alfheimr to finish the chapter.