I think the problem you have is very, very simple: a bad balance, and possibly on both wheels. As you put more miles on the tires the balance gets worse, which matches your description. Have at least your front tire balanced, if the rear tire is fairly new/good, than have it balanced too, otherwise wait to the next tire change. Make sure the guys KNOW what they are doing on balancing. Tell them you want a "perfect static balance".
One of my businesses is a wheel repair business and I see a lot of incompetence of dealerships and tire dealers (cars) when it comes to balancing wheels that cause all kind of problems, and they replace rather a $1500 drive shaft, than pulling the wheels off and re-balance the wheels.
BTW: When I bought my second GrandVista with 1550 miles it vibrated horribly above 75 mph, aggravated the heck out of me! I pulled the front wheel off and re-balanced it; rear wheel was OK. It took 3/4 of an ounce to get in balance, which is a LOT for a small wheel like this. Now at high speed I have absolutely no vibration, So, the KYMCO factory sent the scooter out with a totally unbalanced wheel! It never was off before, of course original tire. Shame on them... So, I bet there is your problem, in bad or unbalanced wheels.