Hey man, it's a well known 'problem' that these bikes have an engine harmonic distortion around the rpms you report (practically all I-4 engines have it between 4 and 6K rpms), but what's weird to me is only the right mirror is vulnerable to vibration. I've read that before, so you're not the only one.
To be honest, I haven't even checked mine that close, but I can tell you one of my mirrors feels somewhat looser than the other (can wiggle it with my hand a hair), so I wouldn't doubt it vibrates as well. Since the mirrors are basically held to the stem with spring washers (so they can fold), I bet one mirror probably has a larger distance than the other, and the springs don't provide enough pressure.
If you replaced your mirror and still have the same problem, I wouldn't bother with a 3rd one. Sometimes engine vibration affects one side of the motorcycle more than the other, and I bet the FJR is one of those bikes since I've heard the complaint before. Other than ensuring all bolts are tight, you could add an O-ring to the spring stack and see if that piece of rubber in there takes care of absorbing the vibration that's affecting visibility. I personally cruise over the vibration zone and that's probably why I haven't notice it, but I'll check next time I take the bike for a spin and report on the issue. Will also check which mirror is the looser one, but am almost positive is the right one indeed. I tightened the black bolt that secures the washers a tad, but wouldn't do it anymore than what feels okay since you can break something. If you haven't touched that nut, first loosen it a bit to break the loctite, then tighten it the max possible with a small wrench so you feel the pressure exerted. No need to put extra loctite, there's plenty in there, and it's the 'friction' kind, which stays there.
One last thing you can do to lessen vibration is to synch the TBs as best as possible. I did synch the TB butterflies, and my hands don't tingle anymore, but feel the vibration (have aluminum custom pegs) just the same, so don't know if it'd affect the mirror or not, but it's worth doing if synch is out of whack at 5K rpms, like it was on my bike. Good luck man.
JC