Welcome to the forum. It is rare (often impossible) for a distant online source, no matter how expert, to diagnose or provide much insight on a health problem that has persisted despite expert professional investigation -- which it seems you have had. But I'll try -- although perhaps not in exactly the way you are hoping.
There are no known STDs that cause symptoms like yours. People often worry about undiagnosed or untreated gonorrhea, chlamydia, trichomonas, nongonococcal urethritis (NGU), herpes, or other STDs in this situation. But in my 4 decades in the STD business, I have never seen a patient with symptoms like yours in which these or any other STD was eventually found to be responsible. In your specific situation, you not only have been tested (I am sure) for many or most of these infections, but have been treated for several of them -- using drugs that are highly reliable.
In my experience, most patients with this sort of problem probably have an emotional/psychological origin, which I call genitally focused anxiety. While I'm not a believer in direct causation of physical pain, irritation, etc by psychological means, for sure anxiety or other stresses can greatly magnify normal body sensations, or trivial ones that would otherwise go unnoticed, to bothersome and overtly painful levels. Then the problem can be exacerbated in a vicious cycle, perhaps especially when various treatments don't work or help only transiently, as did the "meatal vaporization".
I'm not a urologist and am entirely unfamiliar with "meatal vaporization" and what your urologist might have expected from the procedure. For the same reason, I cannot comment on whether it is safe, in particular if done repeatedly.
I am confident your problem was not caused by any infection from the sexual exposures described. If related to those events, I would expect it's primarily through the psychological mechanism, especially if you feel shame, guilt, or other negative reactions to those events.
Finally, I have never had a patient with your symptoms who turned out to have anything serious. Nobody ever later developed cancer, infertility, or any infection that he transmitted to a partner. And also in my experience, once patients come to understand that there is no important health threat for himself or his partner(s), the symptoms tend to fade.
So my advice at this point -- which you should discuss with your urologist before following it -- is to take a few months off, with no attempt at further diagnosis and no repeat antibiotics, meatal vaporization, or any other kind of treatment. During that time, I would recommend you continue or resume unprotected sex with your main partner. As implied above, I think you'll find that the problem improves with time and maybe will fade entirely.
I hope this has helped a bit. Good luck-- HHH, MD
I meant to mention HPV, since you brought it up. There is no evidence that HPV ever causes pain of any kind, and I am equally confident about HPV as for all other STDs.
I'm in the same boat as you. mate. it's been a year and a half in my case. EXACT same symptoms and treatments. at the 9 or 10 month point, the redness and sensitivity subsided considerably, but did not go away completely. the reduction in symptoms did occur coincident with the time I mentally "let go" of my worries. it is not gone entirely, mind, but is entirely tolerable. all the best.