It takes anywhere from 6 - 12 weeks for the neuter to kick in. I think the enclosure idea is great. Heres some other suggestions.
It sounds like Caine is really ruling the roost in terms of your lifestyle and schedule. That is not fair. He may scream to go outside but you need to just let him scream, like a toddler. YOU decide when he goes out, not him. Ignore him, and it will take longer at first, but soon he will realize, you decide, not him, and screaming gets him nowhere. Start making him work for EVERYTHING. Even a pat on the head. He is acting very much like a dog that is the leader of the pack. Protecting his property. Even though he doesnt do it with everyone, just a couple of people is enough of a sign, and once he figures out his strategy works, he will do it more and more. (Im just going by what I have read though)
I think until he is calmer and acting more subordinate, supervise him outside always. For now, I wouldnt do a tie out. That can cause more frustration and soon they become really territorial of their tie out space, and then if someone they dont know approaches that, its really dangerous. I would walk him on a short leash and make him heel, sit, heel, for a few blocks until you let him have some supervised outdoor off leash play. Make him work for every single thing. Make him sit before he goes out, and he cant break the sit even with the door open until you give him a release. And I would contact a trainer and get some obedience stuff going again. You will find with these exercises, he will feel like you are more in control and he can relax, which will make him less aggressive and much less pushy.
If you need me, you can PM me.
I hope this helps.