I use vMix to do events in Michigan.
http://www.vmix.com/software/
They do a 60 day free trial, no watermarks or timeouts - the real product.
Many more features than OBS. Can do streaming and record to disk at the same time.
You can do the chroma key thing, but I find it easier to just do a multiview in vMix with a camera feed cropped layered underneath the match score. When the match is over, the scoring computer full screen will cover it.