Exactly the symptoms I had on my 1999 GS300 with 144k miles.
Rims checked and they were ok, Balanced twice and still had slight shimmy between 65 and 70 mph. all other speeds were good with no shimmy.
Problem was lower front ball joints. both were loose, dangerously so
Had both lower ball joints replaced and front re-aligned now it rides like glass from 35 to 85.
If you have not done so might want to have them looked at.