I think that if you do this and few others do, the main result will be to confuse your readers or hearers -- and of those who are confused, when you've explained I fear that a good fraction of those who didn't already agree with you will pigeonhole you as a crank.
Which is a pity, because it would be good for far more published work to be universally accessible than presently is.
A possibly-better approach along similar lines would be to find some term that accurately but unflatteringly describes journals that are only accessible for pay (e.g., "restricted-access") and use that when describing things published on such terms. That way you aren't redefining anything, you aren't saying anything incorrect, you're just drawing attention to a real thing you find regrettable. You might or might not want a corresponding flattering term for the other side (e.g. "publicly accessible" or something). "There are three things worth reading on this topic. There's a book by Smith, a restricted-access journal article by Jones, and a publicly-accessible paper by Black."
You don't think "privately circulated manuscript" is 100% accurate?
I think it's pretty clear to say "a privately circulated article by Jones and a published paper by Black," at least as long as I provide links. The ambiguity I'm concerned about is where my comment is very short; the typical situation is providing the public version to someone who cited the private version.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.