There may not be a good solution currently, but I don't believe that no good solution is possible even in theory. Which makes me wonder if the VT100 paradigm is holding us back.

Like, if a VT100 understood the concept of tabs natively, it seems like this wouldn't be a problem. Screen could just map its windows onto VT100 tabs, and the terminal would know what to do with that.

I don't know if adding tabs to VT100 emulators would be remotely feasible, or a good idea if it was, but I expect there's something in this space that would be an improvement on what we have.