"Fake" Full-screening a browser window (with no edges) so it doesn't take priority & can have other things full-screened over it?

I'm running a stage show using a projector & Q-lab, and am looking for this solution. On the projector, I need a browser window full-screened with NO visible edges. The window has interactable elements, needs to remain the "baseline", and can't be seen being minimized. BUT, we have brief moments where I need to have Qlab project a video over top, and then back to the browser again. When the browser is in a window, this works flawlessly. When the browser is ctrl-option-F full-screened, the video won't overtake it and doesn't display. The best app I can find still has edges + a bar at the top. I've considered using a secondary zoom-in program to remove this, but it costs $50 and is an extra step I don't want our tech person to deal with. So- Any leads on an app or code that would "fake" a completely full-screen browser window on Mac? Thank you!