Take some time to look into some of the feedback regarding the Kenda 270's. I think you will find many of the complaints echo what you are reporting. I have used up two K270's on the rear. For fire trails and most gravel, it was fine. On hard surfaces, I found I needed to have my seat recovered after approaching any corners the might require any effort to negotiate. I never went down, nor has anyone else I know that used them. A couple of years ago, I located a large inventory of K270's in 120/90-17. I bought about 20 of them for something like $20.00 a piece. Everyone I knew that had 17" rears was running them. The comments were pretty much the same...squirrelly as hell, but not bad enough that anyone was willing to pay retail for a replacement tire. They run 'em until they were slick. I haven't bought another K270 for the simple reasons that I have found other tires that out perform and out last the 270's for less money.
I think your problem may be in your tire. That particular tire is extremely air sensitive. Try adding a few more pounds and see if that does not help stabilize things a bit. That skirm could be caused by the tall, narrow knobs leaning over, especially on the outer perimeter. I suggest you experiment with your air pressures.
“many a trip continues long after movement in time and space have ceased”- Steinbeck, [I]"Travels with Charlie"
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