That sounds like a very good compromise. I hate it when they subject pets, especially small ones to pesticides.
I am glad your husband has caved. Mine would already have the neighbor's cat that we take care of inside if it were not for me and my allergies. He loves her dearly, since he misses our last cat, who was his lap cat. She was an Abyssinian rescue, and they are the most affectionate of breeds. I haven't seen the meme you mention, but I have seen one where the husband does not want the cat, so she is offering up the husband for sale instead.
I am married and own a home now. My experience that was so similar to yours happened a long time ago when I was single, but we presently have what I call a timeshare cat, lol. The cat comes from a home one block away with 9 others and she wants to be an only cat, so she came to our house, choosing the only nearby home with a totally fenced yard that did not have a dog, but did have lots of landscaping to play in and a couple of suckers for cats, ie. myself and my husband. It was obvious the cat was being fed, but not enough, due to her refusal to go home, so we followed her back to her home when she got hungry, and I've become friends with the owner.
The owner provides the food and Vet services, though she gets no shots, due to this woman's religious beliefs, and we provide flea meds during summer, since she does not believe in medications and we got fleas in our house at first. The cat lives outdoors except that it sleeps in my husband's workshop office in a bed he made her which I lined with sheepskin for cold nights. This is central Florida, so she is in no danger.
I am allergic to cats now, so promised the doctor not to get anymore after our last one died, and we are old and cannot afford the Vet bills now, and have no friends left who are willing to take the cat if we pass on. It works pretty well, though sometimes we have to buy food, since she doesn't have time to come over and deliver it in time, and we are feeding only what she wants to feed the cat, which is the very best, plus evaporated milk, which I do not agree with for cats, due to their lactose intolerance, but it is not our cat, so I oblige.
Cats always seem to know how to find those who love them and can't turn them away. They are not only beautiful and unique, but smart, as I'm sure you'll agree.
P.S. I think I told you this before, but I had a cat named Rhonda that looked almost exactly like the one you used to use as your Avatar.