Elite launches in a window for me, so there must be a setting for it somewhere. Alt+enter is the usual windows shortcut for switching full screen windowed mode so you could also try that.
I haven't tried it with Elite, but alt-tabbing to virtual desktop or BigScreen has always been problematic for me. With other games I sometimes have to hit alt-tab so that the virtual desktop/bigscreen window is the foreground app, then hit the home button on the oculus remote/xbox controller twice. Whether you can get back into Elite is another matter. I've only tried it with iRacing and Assetto Corsa.
I've also found with virtual desktop I have to leave its settings window open or alt-tabbing won't work and I get left at a black screen after exiting the VR game.