This sounds frustrating. I will share something that works with Google Meet in the hopes that it also works with Zoom. Our school has desktop computers in each room hooked up to projectors and we are supposed to use a Chromebook that is logged into Google Meet and have that face the whiteboard/projected area so virtual students can see what’s going on. Some of our teachers had the same issues you mentioned and started logging into their presentations on the Chromebook and then shared their screens. Then on the desktop that’s connected to the projector, they logged into the Google Meet so the shared screen showed up for the students that are present. I tried it once and it worked well, other than the fact that the screen ratios did not match up, but that could probably be fixed.
I know this doesn’t solve your original problem and this workaround may not even work for your situation, but I thought I would share in hopes that it does. Let me know if you need me to clarify anything.