I tried to forget the incompatibilities in different old terminal types after about everything settled on xterm compatibility. Instead of running screen, can you run a desktop session under freenx on a server somewhere and run everything in terminal windows there (even ssh sessions that go elsewhere)? If you haven't tried it, the NX client has great performance with freenx, even remotely, and lets you disconnect/reconnect with everything still running. Assuming you have something locally that can run the NX client (windows/mac/linux) you also get mouse based cut/paste and the only down side is a slightly longer time to do the initial screen refresh when you connect.
Hmm, this sounds like an interesting possibility. I don't think we have x-windows installed on any of our server machines but I can look into it. You have gotten the gist of my thoughts here though; being able to return to something I was working on before, without having to log onto every machine again!