Trying to have this discussion without IPA for multiple dialects is pretty tough with "long o" and "short o." I've only ever heard Coq pronounced like /kɑk/, but I'm from the Western US. I know Brits and Americans from the NE have the round low back vowel for /kɔk/. Coke sounds like /kouk/.
I think mostly because to speakers of American English, roundedness is a very important vowel distinction, as “cock” has an unrounded vowel in American English, whereas the others are rounded, except “cuck”, which while also unrounded matches “coq” in position (open-mid vs. open, on the IPA chart)
I was mainly talking about the vowel length. However:
> the “o” in “cock” is the one most Americans would find it most distinct from, I would think.
Really? More distinct than from the "oʊ" sound in American "coke"? (IPA from https://en.wiktionary.org/wiki/coke)