G'Day Henry, I reckon you've answered your own question, but the first thing I'd do is ditch the fairing, most handlebar mounted fairings will induce a weave at high speed, whereas a well designed OEM frame mounted fairing (like my old BMW R100RS item) will generally be of benefit.
I took the "full fairing" off my "boomer" (a "beemer" is a car) one summer and fitted a genuine R90S fairing with fatory brackets etc, and nearly killed myself at around 130 Mph when it got as close to a "tank slapper" as I ever want to experience. I sold the bike with the bikini fairing in place but warned the buyer to keep to highway speeds, but never heard from him after that, so I hope he's ok?
I bought my Suzuki GS1000S (Wes Cooler replica) with the fairing already removed, so I put it back on, and by christ, it nearly happened again! Bugger that, I took it off, hung it on the garage wall, then took the bike out again and crept up to 145 Mph, and it's as stable as a mack truck. All the other possibilities are certainly contributing factors, but my guess is that the fairing is the culprit. Cheers, Terry.