I dug into the issue.. I could be slightly off with my understanding but it looks like PickUpAndHaul basically overrides the default haul job with a job that has pawns put items into their inventory till they can't anymore, then the default haul job runs on the last item they pickup to take the item back to the stockpile. My mod causes the default haul job to not reserve the chosen haul-to tile. So the second pawn hauling the same type of item will pick the same tile to haul to. With both mods enabled together what's happening is the first pawn deposits what he's carrying then reverts back to the PickUpAndHaul job which takes the next item out of their inventory and reserves the tile they want to put their item into, then places the item there. When the first pawn reserves the tile, that tile is no longer a valid deposit cell for the secondary pawn so they cancel their haul job. Usually when a Pawn's haul job is canceled they just gracefully find a new place to haul to, but PickUpAndHaul causes them to drop their inventory items first.

The solution to this issue is to potentially have the PickUpAndHaul folks make slight changes to their mod so it's possible for them to work together.. and/or I have to write code to modify their mod, which means mine can potentially break if they update theirs...