Sometimes, through accident, one of the cats will get outside. Only one time has any of them stayed out longer than 10 minutes, and they were anxious to get back in. We live in wooded area with possums and raccoons.
The exception was out about an hour before he came back. He never again, until the day he died, went near the front door.
Go figure.
We’ve done pretty much the same things (including giving up on furniture). Our current cat will go out on the covered porch but never any further. She’s gotten pretty old as a result.
There are a number of neighborhood cats which certain ladies feed. One of them was coming to my door looking for food and it occurred to me that I should invite it in. It came in and walked about the house meowing vigorously. I fed it a bit and allow it in whenever it wants. It patrols noisily for a few minutes, eats a few bites, then wants back out. I have heard and seen no indication of mice since that first visit. My rodent elimination system costs me a couple of dollars a month for cat food.