That's what I do too. I also have a 12" magnetic plastic folder that's been glued, doweled, and duct taped pemanently open that ends up in my lap while I shuffle pieces around on it. I think it's important to go back and forth between 2D and 3D views. I found using just the computer screen meant a short period of disorientation when I moved back to a real board.
Board or Computer

I have three chess boards/sets that I can have displayed at once.
You can pick up cheap sets for this sort of thing, but the problem for me is more space to have them set up all the time. So limited to 2 or 3 games at a time.

I feel your pain sir. I've got about 20 sets () and even with a card table set up next to my usual table I can only display 5 or 6 at a time. Not sure why I actually need a physical representation of every game I play, but like you I'm just not comfortable making a move until I see it in 3D. Now that we've made the magic 4 post threshold to be seen in the main forum, maybe someone else will chime in.
Okay, what's your favourite playing medium for chess?
Although I am playing against a couple of people on here, I also have the positions set up on a couple of real chess boards, I find it easy to spot things with real pieces. I concentrate more as well with a physical set. Even having a computer display in pseudo-3D doesn't work for me.
But how do others prefer to play?