Boy, this takes me back a few years! My son is 21 now, so its been a while, but I went through the very same thing with my son.
First, it sounds like from your description, you are doing everything right. Remaining calm and sticking to your guns is the right thing. Your son has a very strong will, as does mine. I used to say, "My son has a very strong constitution." That was a nice way to sum up his out-of-control tantrums.
In your situation, it might be a little exascerbated by having joint custody. Is is possible that his tantrums are getting him his desired results at dad's house? Does whoever cares for him do the same when he throws tantrums or are they thinking that he is "cute" or "just being a boy"? Inconsistency can have a negative effect when you are trying to set up a boundary for behavior, if another caretaker does not keep up the rules or consequences you have established. (I'm not judging you for being separated, I'm divorced myself).
Either way, you can still make the rules for your house consistent. Keep doing what you've been doing, and even if you feel frustrated or that you are "losing", you are not. Discipline isn't a magic cure. It doesn't mean that the child will never do it again, it just means that you responded appropriately this time, and next time you are going to have to respond appropriately again, and again, and again, until finally the child realizes that his behavior isn't having any of his desired results.
I have a very strong constitution myself, so my kids got it honestly. They all have a stubborn streak. One thing that was always for sure, whatever they were having the fit over, that was the thing they were absolutely NOT going to have. (So, even if they settled down after 30 minutes like nothing happened, it did happen) So, if they were tantruming over a toy, that toy went away for a day. If they were tantruming over doing something, then they could not do that thing for the rest of the day. They would stay in time out for attempting to bite, kick, throw things, etc. Time out was the consequence of the tantrum, AND taking the thing away for the rest of the day was also a consequence of the tantrum. So, in the end, a tantrum would get them the opposite of what they wanted. After a while, a tantrum just wasn't worth it.
Make sure that they child does not get any attention from you while in time out. Time out is time out. No talking to or lecturing the child. No threatening such as, "Don't you get up, I mean it..." and actually, don't even look at them. Turn your back or walk out of the room. If they get up early, put them back without comment except to remind them to stay put, and turn around again.
One more thing I did, and it became a mantra, of sorts, as my kids were growing up. I used to say, "When you ask a question, the answer can be yes or no." That meant that I, as the parent, had the right to say no to a question and it was not appropriate for them to get angry or have a fit over it. As teenagers, I still sometimes repeat that saying and I get the obgligatory teenage eye-roll, but they still get it. I'm even using it with my future stepson now, and he is learning to back down.
Another thing I did when I saw the tantrum begin to ramp up, I would point my finger and say, "No fit." and sometimes that would stop it. If I saw that the child was struggling to maintain control, I would either suggest that they come sit on my lap for a moment and I would try to talk to them about what they were getting upset about. I'd say, "How can Mommy help you?" or I'd suggest they sit down or put down whatever they were doing for a minute to gain control. The whole purpose behind this was trying to teach them more self control in a situation that was frustrating them.
I hope a couple of these suggestions help. I know its frustrating, but they grow up so quickly, even though it doesn't seem like it right now. Enjoy his growth, his imagination, and his development. Its an honor to be a mother.