So, Rocky has found his niche.
He sleeps in a big basket out in the garage, that's on top of the counter, next to the window. When it gets too warm, he jumps down to one of the shelves below that, next to the vent that brings in fresh air from outside.
He does go outside, but for the most part, he just stays on the cement pad outside of the door. He prefers going out at night, which is not something I'm fond of. He can get the cat door open from the inside if it's set to in only and make his way outside. We've blocked the door a couple of nights with the baby gate, but if we don't put something in front of the baby gate, he pulls the gate away from the wall, and goes outside.
What I have been doing is when I get up at four or so in the morning to open the door in the living room, when I've done that, I go unblock the door in the garage for Rocky. The other morning he was waiting for me, he was very impatient. This morning, he'd pulled the baby gate away and was already outside. I looked out onto the pad and he wasn't there, so he was most likely off exploring the yard.
When we got up and started our day, he was back on the cement pad. I went over to him and gave him a couple of scritches and hugged him. He rolled over on the pad and purred. I left.
The next time I saw him he was back up in his basket.
He now has a routine.