Shooting with a camera and then pausing while recording
It doesn't sound like thee is a cheap or easy way to do what you want to do.
I use premiere a lot and.  There are mutlicam features for Premiere that allow you to sync to tracks and edit them easily, not to do live recording and playback at the same time.
If you stop and start the recording on lulls in the game where nothing is happening you will generate files that can be played back while the computer is recording the next file.

Also
Most computers video cards have an HDMI out, and can output to two monitors.
wire one output through a PVR and use that to rewind etc.  I don't have any experience with a pvr but that might work.