I know but I fear each new explanation will keep raising a new question of its own. Maybe wait till I prepare a proper document.
Or is the inset piece always the same size and shape
Yeah, it is.
The issue is since the background is much lower resolution, you will get jagged seams where the background and superimposed scene are to be blended.
Here's an illustration:
1) Take a lower resolution projection and try to hide the pixels digitally where the higher ones goes
https://i.imgur.com/9sVStQv.png
Now project the higher res beam in this hole. You will get a seam in form of holes.
https://i.imgur.com/zMI9yAm.png
What if you try making the middle beam here a bit bigger to cover those holes? Well you get seams in form of bright intersections because in those spots the light from the pixels is overlayed.
https://i.imgur.com/9ZuP3Ju.png
So digitally, there isn't much option in overlaying two projections, unless they will be very close in resolution (say 720p and WXGA) or if you just need to blend projections horizontally or vertically. But when one projection is bigger than the other in size then even if they are the same resolution you will have this problem.
If, however, there was a way to trim the pixels above which get overlayed in a way illustrated below, optically and not digitally,
https://i.imgur.com/zrSv7ZO.png
then you could easily place the other beam there with almost no seam.
https://i.imgur.com/yDaJd8N.png
One possible solution I proposed is having a transparent film or glass ( which I am not sure exists, at least one with 8ms transition time) which becomes opaque or any other state which can move beam 1 away from the optical path when bright IR or UV light is shone on that film/glass. Then all we would need would be to have that glass be half silvered and project the smaller inset beam also containing IR or UV. Setup would be like this:
https://i.imgur.com/5ku44hR.png
This would solve, or greatly decrease the seam between the two beams.
Any similar solution to this not onvolving pixels would work.
And as said in OP, this kind of beam combining can be also achieved later in the setup by the "projection screen". Or in other words, having the beam 1 section not reaching the projection surface is not the only solution as somehow not displaying the beam 1 section on the projection surface even if it has reached it will also work.
The other advantage is, you don't even have to worry which pixels to hide on beam 1, as they will get blocked anyway.
An LCD matrix or similar instead wouldn't work because there simply isn't one high resolution enough compared to Beam 2, not to mention it has to be bigger than beam 2 which can be anywhere on it, which means you would need an LCD panel with removed backing to be used as a shutter even higher res than beam2. This is what Tom.G. was suggesting, LCD is the most common Light Valve.
If such an LCD or other matrix would be usable we would just make beam 1 such a resolution. I can't as there isn't such a high res projection technology and even if I could the whole project would become pointless, as the purpose is saving pixel rendering time by only having many pixels where needed.
I hope I didn't fail at being clear enough this time.