I know what you mean and I understand your point. You are determined to label the words as exactly as possible while I might not care about how each type of word is called but rather how to put certain words to use.
Nominalizer, noun, whatever... Looks to me like a noun that is preceded by a main clause, which HAPPENS to be translated as either a pronoun or a nominalization of a verb. Your example sentences would seem to me simply like two different possible meanings of the sentence rather than considering there to be two types of こと.
"Deny (the contents of) what I said", that would mean that こと is a noun because
"content" is also a noun. (I don't think that こと is a noun because the English translation says so, though. But simply because it is. Even
jisho.org says so.)
Also, by your logic wouldn't there also be a nominalizing こと? Like in 歩くことが好き,
"I like walking"?
And finally, in your example, it would seem that 言った would require an object, like 何か, to be able to take on the meaning
"deny I said something". 僕が何かを言ったことを否定する. But I might be mistaken here. I probably am. I'm probably corrupted by English where there's the distinction between
"speak" and
"say".
I don't condemn your nomenclature. In fact, most people would probably understand it better if you explained it to them your way (which is probably the standard academic way of explaining this type of grammar). I prefer a somewhat more unconventional approach to it. But then again, I won't be teaching anytime soon (luckily). I might not be ready yet to develop my own methods. However, it does help me the way you write. Just don't be too nitpicky on everything I write. ^^