This is an excellent suggestion.I'm so sorry to hear about your dilemma. Would it be worth it to humanely trap them and get them fixed/shots? (I know that's the expensive option) Any chance of rehabbing them into house cats? I really know nothing about cats; I'm severely allergic, but have been rehabbing a feral dog for a couple years and we've made great progress.
Good luck and I hope your health is not in danger with the bite from Georgie.
I also noticed how you mentioned whether or not you are contributing to them suffering, you aren't. Unless they are very sickly, you are doing a good thing keeping them alive and giving them love. Love and knowing someone cares goes a looooonnnnggg way with animals, even if people think animals don't know anything(whatever bonehead made that up.) Please don't let anyone convince you what you are doing is wrong or inhumane, it's not, it's an amazing thing you are doing for the animals, if the world had more of you, it would be a better place. The ones who are doing things wrong or inhumane is not taking resposibility of their pets and not getting them spayed/neuteured and letting them roam free and face all the dangers of the outside world, those are the people who need to feel guilty, because afterall, we wouldn't be in such a situation of feral animals and pet overpopulation if it wasn't for people like that.