I should think you would have recognized that my use of "denumerable" was at least semi-technical. Before suspecting that I'm using a logico-mathematical term incorrectly, and before going through very many dictionaries, you'd save yourself a lot of time and effort by just asking me what the term meant.
I never once used "denumerable" and "infinite" as if they were synonymous. If you somehow got it into your head that they were synonymous, then I'm not at all surprised that you thought that I was misusing "denumerable".
There's nothing preposterous, in itself, for someone unfamiliar with a word to look it up in one or more dictionaries. But if doing so leads you to suspect that an expert is using the word incorrectly, the thing to do is put your dictionaries away and seek professional help.
You say that my usage "does not conform to what appears to be the more commonplace understanding of the word". Well, how about that! Of course it doesn't. As for your suggestion that I might use "infinitely many" instead of "denumerably many", I couldn't do that because I didn't mean "infinitely many": I meant exactly "denumerably many". Perhaps laypeople don't understand what "denumerable" means; but they don't understand what "infinite" means either. (As I've said in a number of posts here, not all infinite sets are denumerable--i.e., equinumerous with the set {1,2,3,4,...}. Hence the terms can't be synonymous.) So I might as well use the right word rather than the wrong word, and run the risk of foolishly being suspected of using the word incorrectly.