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I’d like to find something that would allow this on a PC

If your PC runs Linux, use x2x or x2vnc. I have this set up at Rio, and it all just works, even the clipboard. If your PC runs Windows, there's a similar thing called win2vnc, but I haven't used that one. Either way you'll need to run VNC servers on all your PCs except the one with the keyboard/mouse.

Peter