This sadly occurs regardless of whether you're using the VIDEO or FILM mode when recording ProRes/DNxHD.
Because of whatever magical colour science BMD is doing, red's simply always look very orange. Just like all the audio issues - BMD is aware of the problems, but there is no information on if or when these things will be addressed.
This can be easily corrected in post, however as you're trying to do live green screen work, my suggestion would be to follow John's advice, and shoot LOG, then apply a LUT between the camera and your CasparCG Server using something such as the
HDLink Pro. Unfortunately the controls within CasparCG Server simply aren't powerful enough to do the correction you need in real time. Or... just stick with your 600D.