How do I get rid of a phorid/drain fly infestation in the cage in a bird-safe way?

Hi all, I'm at my wit's end with these flies. Recently we had to replace a ring in the pipe under the kitchen sink which leads to the garbage disposal. There was a leak, which has now been sealed, and the under-sink doors were left open for a few days to air out. With that said, now drain flies have emerged.

What's worse is that the drain flies are especially attracted to one of my bird's poop. Tons of them swarm, land on her poop, scuttle around in it, and then spread bacteria when they later land on bowls, fruits, counters, and whatever else is in the kitchen. I feel awful seeing my bird with so many flies swarming her cage, so I change the poop pads multiple times a day but it doesn't stop them once she poops again.

I've stopped leaving fruit and veggies in the cage. We've left out apple cider vinegar traps only to find out they're not effective for this type of fly. We have a blue light bug zapper already. We still need to make sure the drain is rid of any nests as well. Most importantly, I'm afraid of pouring a chemical down the drain that will kill my birds.

Has anyone dealt with this before? Are there recommendations for cleaners and pesticides that won't hurt my birds? I've already been clearing out and cleaning my kitchen and the bird area as much as I can without resorting to harsh chemicals.