Suzuki 2 Strokes

Was traveling at 55-60 in fourth. Shifted into 5th and the bike began to violently shake its head. It nearly turned into a full blown tank slapper. I'm well aware what causes this to happen and what remedies this on modern bikes. Do all Gt 's experience it? What helps? Stiffer springs, modern tires ? Was there ever an aftermarket stabilizer ? My psi and rear springs were set properly. I know this isn't new to these bikes, but what r u guys doing to smooth it out?

I can't help but I've had my 550 over 80mph a few times without any problems.

I had a 550 and a 750 back in the day.....very early 80s, and used them as hard as they would go....never experienced anything like that at all. I've had lots of 500s since 77, and had a couple of head shakes on the T500 with silly big bars on rubber mounts, but that's it.
Many of my mates had the 550, and I don't recall those characteristics at all, I would think you have some underlying issue there.

Tire pressure, wheel alignment, wheel balance, swing arm bushings, rear shocks, steering head bearing play/preload is what I'd be looking at.

Found my excessive head shake at higher speeds problem. The collar lock under the top triple tree was loose as a goose. No shakes, now.