Following a lengthy six month battle, I haven't seen a single fungus gnat in about six weeks, which means I've either won or they've evolved to be invisible, which is also a win. Dearest plant parents, this is what worked and what didn't.

Essentially, the killer combo was a mix of biological and conventional warfare. Yellow sticky traps at the soil line to kill off any adults, and infusing water with mosquito dunks then watering weekly. The dunks water is a little annoying because it requires planning (you need to let it infuse overnight) but once I got in the habit it's worked a charm and it's great to know it kills the larvae really horribly and painfully.

The most horribly affected plants (Lana del Rain the raindrop peperomia, Figgy Smalls the bonsai ficus, Frank the Chinese money plant, and Callanis Morrissette the calla lily) all got a hydrogen peroxide soil drench (1 part 3% hydrogen peroxide solution to 4 parts water), then repotting, then another soil drench for good measure.

The things that didn't work were:
-Diatomaceous earth. Expensive, inconvenient, and despite a thick layer which was kept dry, neither adults nor larvae were harmed.
-Sundews. Love the little guys but they require sun so ended up living next to the succulents. Had to tweezer dead gnats off the traps to feed them.
-Neem oil. It smells terrible and it doesn't do anything.