Redirect existing windows via SSH and X11 forwarding?

It looks like xpra is an active successor to xmove, and does exactly what you want. The devs bill it as "screen for X clients". While it needs to run on your remote server, it runs just fine out of a home folder. Besides python, xvfb is a runtime dependency.

Once you get it installed on the remote server, it's pretty easy to use.

xpra start :8 --start=xeyes

On your local machine, run:

xpra attach ssh:YOURSERVERHOST:8