This is the first vibration issue I've heard with a Toyo tire. Though every manufacturer, no matter how good they are, have a failure now and then.
I've got over 3,000 miles on the Toyo T1R and it has been smooth as silk from day one no matter what tire pressure I use. Instead of having it balanced I pulled all the weight off and put Ride-On in (on Lamont's recommendation). I was surprised but Lamont was right! How about that!?
Not only does it save the cost of balancing but it balances the tire over a wider speed range and will self adjust as the tire wears (which weights cannot do). Not to mention the benefit of flat protection.
Until your last post I was thinking it could be a bad balance job (it happens) or a bad tire (this too happens).
But pulling the clutch in at speed will not alter either of these conditions so I'd say you have effectively ruled out the tire or balance as the source of you problem.
Pulling in the clutch at speed will greatly affect belt vibration. If you're sure your pully is good I'd say belt tension is your problem. Especially since you did not have this condition before changing the tire (and most likely changing belt tension).
I have been surprised at how much you have to screw the tension adjusters in or out to get significant change in belt tension. Actually, this is a good thing since you can get a very accurate adjustment.
Without some way to measure tension you are really working in the dark. I adjusted my belt from 260 lbs. to 200 lbs. before my trip to Cuba and it changed my vibration issues quite a bit. I'm not happy with it so I'm going to lower it to 180 and see what I get.
I suggest getting a gauge so you have some idea if, and how much, you are really changing your belt tension.