I see it's been a few days since you made this post, but if you're still following, I'd love to hear a little more about the cultural distinction you're making there, and what it means to you.
In the US, the term 'Chinglish' doesn't really convey the same range of meaning(s) you're attaching to it here. Sometimes, you'll hear Chinese-Americans use it to refer to the mix of Chinese (usually Cantonese) and English their family perhaps speaks at home; but just as often, it's used by Americans of any background to refer to what we (stereotypically) perceive as "kinds of mistakes Chinese people who can't speak much English make when they attempt to." Most Americans would never have heard of the English-based creoles spoken in Singapore and Malaysia, and those who have generally call them 'Singlish' and/or 'Manglish'--I think most Americans would hesitate to call them 'Chinglish,' since that word is perhaps somewhat tainted in our culture by its potential associations with pejorative, 'laughing-at-rather-than-with' associations.
But, it could also be the case that there are pockets of Singlish/Manglish speakers in some Chinese-American communities out there who
do use the term 'Chinglish' to describe their 'creoling,' and I'm simply unaware of it.
I'm a white/Euro-American currently winding up a year working and teaching at a Hong Kong university, with frequent visits to the mainland on related business. Unfortunately, like most white people here in HK, I can't speak either Cantonese nor Mandarin worth a damn, lol; so I'm afraid I have relatively little of insight to contribute concerning the culture and politics of multilingualism here in HK. I teach in English, of course, but my students have been roughly a 50/50 mix of mainlanders and 'HK people' (i.e., HK ethnic Cantonese)--that's a considerable overrepresentation of mainlanders, relative to how many of them are actually enrolled at our university overall, but in general, we find our mainland students more keen on signing up for the small number of courses in English we offer, since they're more driven to really work on their English. (To be fair, as you'd expect, our HK students do tend to have better English heading into college to begin with, though they're by no means reliably highly fluent: while English technically remains an official language here, just as it does in Singapore, it isn't at all the full-fledged
lingua franca it is there, where the majority can speak it with ease regardless of what else they speak at home...instead, Hong Kong lives, moves and breathes in Cantonese, so if you don't want to live in a bubble here, you'd better learn it, otherwise your social circle will be limited to some fairly elite connections.)