this presupposes that you know how the speaker pronounces 'shot and shop and Ron and Don.'

Yes and no. We don't know from this description how Jenet pronounces the word "shone" at the phonetic level. But the US/British distinction here is phonemic.

But your main point is correct - sounds in general and these vowels in particular are notoriously difficult to discuss in a text-based medium, because of the amount of regional variation, and assumptions that turn out not to be universal. For many Americans, "stock" and "stalk" are homophones, hence punning titles like "Silk Stalkings" and "The Squawk Exchange", that are incomprehensible or laboured to the European ear. So you can't really convey a pronunciation by appealing to the pronunciation of another word, unless you are pretty sure of how every reader pronounces that other word.