I was hoping to see a picture or drawing of your cable and eyelet idea.
I cut my vibrations down majorly by a combination of things:
1. truing the wheels and adjusting the bearings and cones
2. trying different spark plugs
3. using a spring chain tensioner on the motor side.
4. using a fatter front tire.
The spring tensioner did the most, since the motor chain is dampened by the neoprene idler wheel and no longer telegraphs the severe vibrations of every engine cycle to the rear of the frame or the seat tube.
The fat front tire did a lot for comfort and cut a lot of road buzz.
re: chains. I recommend throwing away the kit chains straight away and using a KMC Z chain or other good quality common chain. If you have the money ($30-40) you can get a BMX half link chain (entirely made of half links) that will ride well and probably last longer due to even stretch.
Use a common ruler to measure chain stretch, or a Park chain checker. With a ruler, measure from center of one pin to the center of the pin closest to the 12" mark. If its over 12 1/8", or starts "shark tooth"ing the teeth, pitch it and get new cogs.
With these motor kits, it might even be able to stretch a little more and still make do.