That's great that classic is running, I seen last months pic post, nice machine.The Moped Army Forum seems to have the help available for damn near any problem,
Heres my two cents, spend it the way you want.
The high speed vibration could be:
flat spot on old tires... (unless new)
flat spot on chain........(unless new)
my bike won't start either, unless it's moving
adjust your idle screw (when it's warmed up)
clutch engagement too tight
fuel valve leak
disc brakes in 63?
put on center stand and work lever/pedal while running, see earlier posts about soft brakes.
not holding your mouth right
listen to what these guys say,
in no particular order: