I know this is going to sound like one of those generic troubleshooting answers, but have you tried plugging/unplugging the hdmi cable or turning on/off the tv while the ossc and game console are on? It may be sort of a handshake issue with hdmi input on the tv and the ossc. Sounds similar to issues people have had in the past with older tvs and hdmi using devices like cable boxes, etc. There are a few topics in different av forums on the internet describing a similar issue to yours.
Either way I hope you are able to solve it, I haven’t seen a lot of people talking about using the ossc on an hd crt and am curious to see pics of how the image looks, and how the input lag is.