There's plenty of easy ways to do this .. I v've it done it both at work (where we have 3500 of them) and home (to overcome Crhomes socket limit) .. but it's basically just a reflector. A websocket works best and if just one feed works fine, this being sort of how earthcam, et.al. work.
For this the best thing would probably be to use the ELB backwards to pull ONE feed from the (obviously not local camera as it's aws) or Nginx and then create (however you're doing this, eg: docker doing all 4, 1 for each, whatever) internal endpoints that get a copy, this saving vastly on outband bandwidth for you. Then ffmpeg handles remapping the stream to desired size, quality, format, whatever and passes ro nginx (that's a good choice) plugin, the selection of which being a simple CSS or Javascript menu (I do what I can to avoid JS). Can also grab static to handle LoS or timelapse. What's it for? .. might have other interesting ideas.
I can just advise your infra folks what I need, can just give you the REST commands to run in curl to copy/paste or I can screen shot through it I've got lots of things there.
I know I'm a new face but we all start somewhere. spent a decade as head IT security guy at a bug university, I'm easy to verity .. csuohio dot edu slash security .. was me until recently. Or google my name.
I will mention though I'm a bad UX designer but good at all but that .. I'll deliver basic page in whatever lang and you make pretty, if existing I can integrate however.