I had a wobble on my 07 rkc before I put the throttle up
touring stablizer on it, now wobble gone

 

the 07's have a problem at high speed in the twistys. It's because the way the frame is set up where the trans and the swing arm are not directly attached . They sell an aftermarket piece called a tru-track that bolts up the swingarm andt the tranny the website is either tru-trac or tru-track.com. good luck