Turns out the success that I reported over in the Steam forum (didn't know there was a separate Oblivion forum at the time) was short-lived, as I can now launch the game without incident but have no reliable mouse input. That is, the tracking of the mouse is very exaggerated--movement the mouse a short distance will result in the pointer moving across the screen, and in a direction skewed from mouse input. I have tried a couple of the solutions suggested here, to no avail--although I see all of the solutions offered were for versions of Crossover before 12, which is where I started.
In case you didn't pick up my topic in the Steam forum, it's here:
https://www.codeweavers.com/compatibility/browse/name/?app_id=206;forum=1;msg=156597
And, to be clear, I was able to run and play the game without incident just once after I upgraded from Crossover 12 to version 13. I have been having the mouse input issue since then.