I've found it is far to easy for a game (and/or wine) to mess up the resolution and (multi-)screen layout.
Because of this I always set the "UseXVidMode" and "UseXRandR" registry keys to "N" in the wineprefix (see:
winehq wiki).
With this, for me, Elite runs fine in a borderless (primary screen sized) window, no need to use the wine virtual-desktop.
I'm also not experiencing any problems with alt-tabbing or switching virtual desktops.
And I also want to say a quick thank you to the people here.
I don't use or have windows so I was rejoiced when I read the success stories. That was around last Christmas.
At that time Elite was on sale so decided to give it a try. I have been playing it almost daily since then.
Thank you! o7 cmdrs!