Farmers will tend to carrots/potatoes, but not wheat/beetroot

Placed in a 9 block radius diamond with a bed, and a trapped villager across hopper minecarts to catch crops with a bell behind them. Both farmers have identical setups, but the carrot farmer is industrious and produces regularly. The farmer with wheat barely farms, and never throws his crops to the trapped villager, unlike the carrot farmer. Over multiple hours of gameplay, I have received numerous stacks of carrots and not a single wheat from the farm system. As a note, the carrot system is on top of the wheat system, so it's not a feeder issue