Ralphie here is a idea for your squirrels . In the 80's I worked at a seed and hardware store . In the summer city people would buy live traps to catch chipmunks . They would release them in the park . Then people living near the park would come in to buy live traps complaining about all the chipmunks .

So maybe you should catch squirrels and move them to the city .
Or you could get bigger cats . Like Maine coon cats or Norwegian forrest cats .
I have threatened for years to live trap critters and release them in the cities or suburbs...
I am quite happy with the cat I have. She does not demand attention, other than a back scratch when I feed her and her spawn. The spawn are scared to death of me, which is even better. The cat will not come up to me in my machine shed or outdoors, she is never hanging around us on the deck or in the yard. Who could ask for a better cat?
I tried to remove a few squirrels from the breeding population yesterday. I know 2 of them are most likely going to smell this spring as they limped into holes in the tree in the front yard....
I have one I have to go retrieve and clean for supper. Judy will be so thrilled to eat squirrel tonight! (not).....
There was a dozen out here again, I knocked on the window and they ran away like squirrels should. Apparently, the episode with the 22 yesterday has them behaving properly. A few went into the trees outside our bedroom window....I being the great white hunter, snuck into the bedroom, slid the window open and saw my game in the oak mocking me.....
I slowly raised the rifle to my shoulder, put the iron sights just under the monsters head, braced myself for the heavy recoil, took in a deep breath slowly released half the breath, held it and squeezed the trigger ever so gently. I immediately felt the pain of the shell igniting in the chamber as the rifle was pushed back into my shoulder...
When the smoke cleared I saw the monster, fall forward and tumble to the ground, landing in a soft cushion of wet snow.
Ding dong Ding Dong the monster is dead!
Now I simply have to put on my boots and snowshoes and sneak out and find his body so I can properly prepare it for the little woman's meal...
Life is good.