Thank you both for your help, this method is not bad at all.
But I would much prefer not to "disable" the other display entirely this way; I can see that it means that I have to set the active display as primary, and that means moving all open windows there.
So, although I know I'm being a little "greedy", I'd like to clarify my hope a bit: Is there a way to simply
blank one display at will, without causing any windows to move around?
I really only want the video player to show up on my projector, and I'd like for the other windows I already have open on the monitor to not be shuffled back and forth, forgetting their positions, etc.
I suppose I might set up windows profiles for them all to avoid this, but that seems needlessly complicated compared to what I actually want to do - and I could probably never get all of the possible windows I might have arranged that particular day into a profile.
Once again, thanks in advance for taking the time to read and think about my question.