Detachable shells in Emacs?

[Sean McAfee <eefacm@gmail.com>]

At my workplace, I often invoke commands in my Emacs shell buffer that
take quite a long time to finish--sometimes quite a bit longer than I
originally expected.  For example, on Friday afternoon I might find that
the command that's been running for an hour is going to continue for
several more.  I'd like to head home for the day, but I'm interested in
all of the output, and I don't want to interrupt the program to start it
over, perhaps because it's making changes on a remote server and
interrupting it could leave things in a weird state.

What I'd like is to be able to detach the shell process running in the
buffer, like the GNU screen program allows me to do, and resume it
later.  I tried the direct approach of simply running screen instead of
bash in the shell buffer, but screen won't have that: it complains
"Clear screen capability required" and exits immediately.  I scanned the
various options to screen to see if there was a way to invoke it in a
relatively feature-free mode that doesn't support multiple concurrent
windows, but didn't see anything relevant.

I could run screen inside an Emacs terminal buffer, but I prefer
shell-mode in general for various reasons.

Does anyone have any thoughts?  I feel I could probably contrive
something useful with enough time, but I wanted to see if any
approximately equivalent solutions already exist.