Now I’m using a Monoprice 8x1 HDMI switch, and I wrote a little app to control it from my PC over serial cable. It lets you bind each input to a hotkey, so I can switch both my OBS scene and the HDMI input using a single key and no remote controls. Here’s the app on the off chance that it’s useful to anyone else:
Monoprice 8x1 HDMI Controller App on GitHub
Any USB-to-RS232 cable should work fine. I use this one, no problem even with a long USB extension cable.
UGREEN USB to RS232
No clue if it works with any of the other models of HDMI switch.