Thank you, David. To bring you up to date, I've spent the last couple of days making Gnome usable enough to get work done (mostly that meant copying in my Thunderbird and Firefox . directories, several tries at cxoffice, an NFS mount of my real home directory, and a big learning curve. I do not like Gnome's handling of workspaces!
cxoffice has been a disaster. Installing version 21 and copying over .cxoffice didn't work. I moved .cxoffice out of the way and started with a clean office bottle. Exporting the office bottle worked fine but importing it hung halfway through (and I checked that there was room on the filesystem). So I did a clean Office 2016 install (activation problems notwithstanding, it's good for a few days.) The resulting Office was highly unstable, Word and Excel would crash/vanish for no obvious reason, sometimes Word was missing fonts, sometimes it took 100% of CPU.
I tried to keep a couple of spreadsheet open in workspace 4 while doing actual "work" (email and web surfing) in workspaces 2 and 3. I never did get the kind of ghost cross-workspace behavior I get often with Xfce. So I believe the problem I'm having is likely specific to Xfce.
I did have one strangeness with two Word windows and a PDF reader open. Excel had just crashed. My PDF was the active window but dragging it it displayed behind the Word docs. Then a Word window had a visible forward border (similar to what I see on Xfce) on top of the PDF but the PDF content was otherwise on top. Then Word crashed and both windows exited. All this was within Workspace 4, not cross-workspace. And I doubt it would reproduce.
When you suggest a clean Gnome install, presumably you mean a clean Ubuntu install, not xubuntu? I can do that if you think it will help a lot, but I'm pretty sure the problem doesn't appear under Gnome, and that's a full day of work to download, install, reconfigure, etc.