First of all, this is a GENTLE parenting discussion, right? On that basis, I'll give you a gentle parenting option - I'm not sure that holding a door shut on your toddler or yelling at them etc is what I'd call gentle. It's also debatable of course, but I don't think time-out is preferable either. Time IN maybe where you add time with them rather than taking it away.

We have problems with DS hitting, kicking, throwing things etc. In his case I think it only happens when he is particularly bored or unsettled - I would imagine in your DS's case, life is pretty unsettling to him! THis might just be how he is letting you know.

You could

a) try responding to him when he does something like that with "hitting (or whatever) is not okay. Are you feeling angry/sad/bored/worried? How else might you be able to tell me that?"- i.e. try using it as a moment to teach him how to express what worries him rather than acting out. My nephew responds to this sort of conversation REALLY well, it is surprising!
b) Get those "When I'm feeling..." books by Trace Maroney to help him learn appropriate expression of feelings & frustration
c) Make your own little book to read with him with photos of himself doing lovely things and write a very basic story about what to do when he's frustrated. (We did this on a diff issue with DS and it has helped!)

I just realised those points might be quite long-term goals for you if you are looking for an immediate thing. I guess that's part of my philosophy. It's important to tell them it's not ok in the moment, but even more important is helping them to learn what IS appropriate.
Just saying "NO" doesn't achieve much IYGWIM.

I hope that helps a bit...........

I get really frustrated too by the way. A friend said to me recently that sometimes the negative attention that comes with these things is less helpful than just ignoring it. It feels wrong to me to ignore it, but I get what she means. If your DS is looking for attention then it is good to give it in positive ways - like reading time, building, whatever he likes to do so that he's not trying to find it in destructive ways.........

Hopefully he settles down when you get home! Good luck!