Try the Deep Color change and see if that doesn't fix the issue with HDMI 2. It sounds like you are on the edge of bit errors and that may help.
I'd still want a working HDMI1 since it is likely the same system board as HDMI 2. At least this way you can pick the time for the projector to be away rather than having it forced on you by HDMI 2's failure.
As far as cat 6, I don't have a preference for this application. Any true cat 6 should work for 50'. However, I'd try the Redmere active HDMI first since I'd want to keep from adding more adapters, when possible.