If you can find a motorvation Formula sidecar. Excellent look, flip up nose, the formula II handles a top. I had one on my '85 Kawasaki Voyager and it handled fine when it was empty. With it set up right you should not have too much tugging to the right. If you change the forks to leading link on the GW that will help with handling and any head shake. I had the straight forks and didn't have any issues. If it did shake a bit at low speed it was usually due to road surface and a bit more throttle made it go away.
Scott in Shoreview
'79 Suzuki GS550