About GBI-ULL, I recall it had different line count than usual 240p (can somebody post its sync details here?) which explains why it may not work with some displays in some modes.
960p is not a CEA (i.e. HDMI) mode, so TV’s probably have more tolerance there if they claim to support (VESA) 960p.
240×4 and 480×2 generate quite similar output, so if only either one works then the other’s parameters could be tweaked until output is ok.