Another thought - beware the culling out for predation due to boredom's sake rhetoric. Most of the hunters I know don't actually need to hunt. That's not to say they waste meat, but they hunt because they want to, not because they will starve if they don't hunt.
There's hunting for sport - which would be most of us here - then there's just killing every darned thing you come across that you can kill because you feel like it - which is every feral cat out there.
As sportsmen and hunters we only kill what we have tags for or what is allowed for us to kill during the specified season and that we have licenses for. We have a bag limit and a possession limit and we obey those limits. We also don't kill random song birds, protected species and anything else unfortunate enough to cross our path.
Feral cats on the other hand have no concern for tags, seasons, bag limits etc. They don't give a darned if a bird is a song bird, game bird or freaking protected species. They just kill it. Seen plenty of them stalk and kill then leave the carcass lay because they just saw the prey. That was really what proved to me they should be destroyed on sight.