If you are doing cable runs of more than 15-20 ft, I would probably use SDI. It's just going to be much more reliable, and since it sounds like you are going to be doing HD monitoring anyway, the HD-only HDMI to SDI converters are not that expensive these days.
I'm not sure what switches you are thinking of using, but keep in mind that most of the lower end video switches do not do clean cuts between different video sources. And some can take several seconds to lock to a new video source after switching which may mean seeing a black screen in the interim. This can be pretty frustrating if frequently switching sources frequently while monitoring.
I think you would probably be happier with something like a MultiView HD or MultiView 4 which will allow you to monitor all 4 sources simultaneously in a quad-split view on an HDMI monitor or TV. With the MultiView 4 you could use a 4K screen which would mean each quadrant would be a full 1080p image.
In terms of timecode, the Pocket 4K can read LTC timecode from an audio input, which is nice. The GoPro's unfortunately do not have any built-in timecode functionality, although there are some 3rd party solutions like Timecode Systems SyncBac Pro which add timecode capability to various GoPro models:
https://www.timecodesystems.com/how-to- ... pro-hero6/You will need a timecode generator of some sort, which could be an external LTC generator (in which case you would feed this into your ProTools system as well as sending this to all of the cameras). You could also probably use the ProTools system as the timecode master. I think the official ProTools solution for this is the Avid Sync HD hardware, but you might also be able to get by with a MIDI Timecode (MTC) to LTC converter like LockStep (
https://figure53.com/lockstep) or Horae (
https://sononum.net/horae).