Hi Fletch -
Vibrations with these engines have contributed to many a rider's problems. Over the years, different recommendations from different builders have been offered. Some fix action that worked for one rider did not do a bit of good for another rider. If you go through the multitude of posts over many threads addressing vibrations, you will get the idea.
Here is what I offer in my own long-winded way:
Bicycle frames can be very different from one model to another. Tube wall thickness is a big, big factor. The thin wall tubes on lightweight bikes are a fraction of one millimeter thick from the bikes I have cut up. Thicker is better. But you don't learn that until you cut a bike up. This is usually avoided in a normal build.
Both the down tube and seat tube will flex back and forth a little bit when these two cycle engines are running, mounted to the center of the tubes. These mounting tubes are not bedrock solid by any means, and their movements at the rate that the engine is running are the vibrations that always have negative effects, as you are experiencing. In my early riding days, I did not take my bike's two cycle engine above 4200 rpm (measured by electronic tachometer) because the vibrations just escalated out of control above that range. Vibrations were tearing my build efforts apart.
My fix: Stop the engine from rocking fore and aft on these flexible tubes as it is running.
Here is what I did: I removed any rubber padding from between the frame tubes and the engine mount points. I mounted the engine directly to the tubes: metal to metal. The engine still vibrated badly. Here is where I got unconventional: I got a pair of kinda small-sized turnbuckles from the local hardware store (Ace was first choice). I also got some solid steel wire, around 14 gauge or 1/16 of an inch diameter. I fashioned a "noose" with these items.
Open the turnbuckle eyes as far apart as they will go. I looped a wire length from behind the seat tube / top tube welded joint to both sides of the engine cylinder. I ran another wire around the front of the cylinder, between upper horizontal cooling fins. The ends of the cylinder wire were looped through two turnbuckle eyes, one wire per eye, one turnbuckle on each side of the engine. Ends of the tube-looped wire were looped through the other turnbuckle eyes. Wrap the wire ends so they will not slip out of the turnbuckle eyes. (Try to position the turnbuckles so that they are not in contact with both sides of the engine. My fix does have them touching the cylinder, but there is no ill effect.) HAND tighten the turnbuckles equally, drawing the "noose" around the front of the cylinder tight. At some point, you will start pulling the seat tube and down tube out of perfectly straight alignment, but the bends will be so very small, you will not see that. When it takes effort to twist the turnbuckles by fingers only, stop tightening. (I can't give you a hard, measurable number; it is a "this seems about right" judgment.) You don't want to break the cylinder off the engine crankcase.
By doing this, you remove most of the engine's ability to rock forward and backward while running. Hence, vibrations are minimized; the steel wire and turnbuckles will not lengthen. You "lock" the position of the cylinder and the rest of the engine to a position that allows almost no forward and backward rocking.
This offered solution is unconventional, to be sure. I have not heard of any other builder apply the same "patch", if that is what you want to call it. But this worked for me. I have raised my top measured engine rpm from 4200 to 5800 without the nasty vibrations that were present before. Riding my particular bike is much more pleasant. I now ride it routinely in the 5000 rpm range; I never did that before.
Try this, all parts will cost less than $10. It is not difficult to install, but it is a snap to remove if this does not work for you.
I hope this helps.
MikeJ