Hi @MattB,
Getting back here again. Yay, Shotgun Create is the first thing to look at for screen capture, Screen Capture in Shotgun Create. As for live show of game play, you probably want to try with meeting/webinar tools, which support desktop sharing.
Checked with the team that there is currently no plan for a new integration with Perforce. You could follow the post to submit it as a feature request.
I would also recommend you to post in the Pipeline Integration
category as well as some of our clients are enthusiastic in self-development and may have done or are doing something similar.
Cheers,
Ben