I got materials for an iron farm and looked around for a spot to build it in creative mode on a copy of my world, then decided to experiment a bit to see how well it works here
The rates are pretty good and it completely prevents the cat problem I was worried about, gonna have to wait a bit for the redstone part though. All that does is filter out iron and poppies to turn them into bone-meal and iron blocks. Don't have a way to filter out string though so that'll just have to stay in the top chest