Cat has been caught.
Traps didn't work, I even tried a drop trap and a medium dog carrier with a string tied to the door. I sat holding the string and watching the make-shift trap for up to 3 hours, and it would only stick his head in. It did like KFC, it came running when I put it out, but it refused to go inside a trap to get it. I've been feeding it and gradually moving the food deeper into what ever trap I was trying, but its a cautious cat.
This time I put food in my garage and hid behind the door and waited for it to come inside. I tried this once before after it was suggested on this board, but it was unsuccessful. This time it worked, maybe because I tried during night time.
It walked in, and even smelled my shoe. After slamming the door once it got in far enough, I caught it inside a mesh laundry bag and shoved it into the dog carrier, only a minor scratch on my hand. Covered with a towel, food and watered until morning.
I think this is a neutered cat. I didn't get a good look at it, but it has that sagging belly skin I usually see in neutered cats. And its a big cat, at least 15lbs, maybe why it wouldn't go into the traps.
Thank you again everybody for the ideas and encouragement! My family is very greatful. Not only do we feel safer, but I'm glad the cat won't have to suffer through the upcoming la nina winter.