Pretty much, he's done. Go ahead and put him to bed tonight in the crib. But no more time out in the crib. See how he does. If he doesn't climb out, perhaps you have a little more time for night sleeping. If he does, then no more crib.
Do you have a gate you can put in the doorway of his room? Maybe he will climb that, maybe he won't. I'd use it and just make sure his room is very safe for his time outs. You are doing the right thing, putting him in his room during scream fests. You don't want him to ever get what he wants when he screams, and you don't want him to have you as an audience when he screams either. If he starts climbing the gate, time to shut the door. You can hold it on the other side - if you are quiet, he won't know that you are out there holding it. Or, you can turn the knob around and lock it from the outside. Never let him know you are outside the room - it negates the timeout.
Now for the crib - time to put the crib mattress in the floor and take the crib out of the room. Let him sleep there for a while, and when he's a little older, either get a toddler bed, or buy a regular twin bed. When you buy a regular twin bed down the line, go to the store and pick out several choices of what you would be willing to have. Then take him and tell him that he's going to get a big boy bed. Let him pick from your choices. It will make him feel very good to get to help choose.
If you start having trouble with him staying in his bed, I would require that he stay in his room, but let him sleep wherever in the room he wants to. When he realizes he's not getting out of that room, and you aren't paying attention to where he's sleeping, he'll get back in the bed because it's more comfortable than the floor.
D., there is nothing in the world wrong with locking the door so that he can't come out. It is a safety issue for him to be wandering the house, so you must keep him in his room when he is supposed to be in there. Don't feel bad and don't feel guilty. Just make absolutely sure that he can't hurt himself in there.
Dawn