So, I started up a savegame with only the required mods and tested various contracts on fields in that section of the map over many months.
In order:
Field 56: Cultivating = Total completion WORKED
Field 57: Spraying = DID NOT WORK
Field 60: Cultivating = WORKED
Field 61: Spraying = DID NOT WORK
Field 60: Stone Picking = Total completion WORKED (Was worried because it started with some % done and splotchy [which is actually more what I'd like, so if that's on purpose I love it even more lol])
Field 59: Harvesting Red Beet = WORKED
Field 57: Hoeing = Total completion WORKED
Field 61: Fertilizing = WORKED (liquid)
So of the jobs I did, it was only spraying herbicide that didn't work even though other jobs on the same field did work. Hoeing did work so it's not just weeds (although the hoeing job was done before weeds came up if that makes a difference with whatever it is).
The spraying contracts allow you to spray (there is no "you don't have permission" or whatnot) and you will use herbicide, but the weeds won't die.
Sorry I don't really have an idea what would cause it, but I DO know it's not the entire map. I for sure have done spraying contracts on Fields 41, 28, 6, 30, 49, 50, and 36 without a problem on my real save.
Edit: I went back in to that save and bought Field 61 (which had visible weeds at the time) and they did die when I sprayed them so at least owned fields work there. :/