Solids and poops and washers oh my

EBF baby is taking to solids well. Problem is, poops are ruining my diapering routine. There’s usually one turd I can flush, and then the rest is very chunky and sticky. I have a sprayer, but I hate using it because it just makes the diaper soaking wet but leaves poop in the diaper. So when I wash the diapers, all the bits of food are still in the diapers, even after they’re clean! Plus, I have sopping wet diapers in my dry pails. Do I need to switch to wet pails from here on out? Please help!