Zoom meetings: how to eliminate gray boxes?

I figured it out myself, with some experimentation, running as host and participant in the same meeting. The solid dark gray boxes are clearly a security mechanism by Zoom to prevent participants from seeing other windows on top of the shared window.

Why should participants be able to see other windows, you ask? Well, it's simple and complicated at the same time. Instead of simply sending the video being shown directly to the participants, Zoom intercepts the hardware to capture the data as it is being displayed. So you see the topmost shared window AND any windows that are on top of it! Graying out the window prevents participants from seeing whatever the host is doing, for security.

So the solution appears to be pretty simple: just turn OFF the "optimize for showing video" option. Then Zoom simply sends the shared window, again and again (at 6 to 30 frames per second, depending on source and destination bandwidth) to the participants and ignores other windows. In fact, with Optimization off, you can even minimize all windows and/or return to the desktop, and the participants continue to see the shared window only.

For the Zoom meetings I host, I want the best experience for my participants, so I set up muting and other options the way I want, then I show the video in a video player, share the player output, and optimize it. I make sure that all other windows are never displayed on top of the video on my screen while the video is running, and I keep the cursor at the extreme lower right so it is not seen. I avoid any use of the cursor or of Zoom features while I am playing a video. This works perfectly for me, because we don't use chat or other features when playing videos.