That works as well.
If you "extend" your desktop, you can just drag the second instance of MT (logged as a player) to the 2nd monitor, hit full screen, done. Leaving your laptop screen to run MT as a GM and moving all the tokens as needed?
This is what I do, but NOT as a player since the token cannot cross the vbl line (see OP) or i am missing something else. However, it can if log in as a DM and then use player view. Works well for me.
The "switching hassle" was only mentioned because i would like the mouse to stay on the second screen just to speed up moving, revealing and zooming.
I've been away for a few years, so i'm re-learning
Nice to see all goes well with MT and you guys still doing a great job.