Hey. Sorry for a delayed answer...
Well, God of War 1 doesn't have a real NG+ mode. Just using a costume is the closest thing to a NG+, and that's what Exe and others have started calling any GoW1 category with a costume. And since you can't wear a costume on God-mode, God-mode and NG+ are basically incompatible.
So what you're asking is... God-mode glitchless any% category? Guess that would be a bit like what Ballofsnow's classic God-mode run was like, except not segmented. That would be a valid category, I guess, although "glitchless" is a bit hard to define. It could work out, if there were interested runners.
As it is known, God of War 1 on PAL (European) and NTSC-J (Japanese) versions has some cutscenes that are censored. These censored cutscenes are shorter than the ones on the original NTSC (American) version, which means runners playing on these versions are at an advantage. Specifically, glitchless
