Ah, nothing like a chopper with an extended front end and mild rake to handle those sweepers!
After I got my Venture, which had set in a damp machine shed on soil for who knows how long, I experienced "shakes" when slowing down, passing through a certain speed. If I released my grip, it would try to wobble. I replaced the front tire, which took care of the problem. It fast sweepers, however, it did want to wander slightly, and reading the Venture forum (link on my 'Me' page) I found out that was a common problem, easily fixed with a heavier fork brace. I found a "SuperBrace" here on ebay and haven't had a problem since.
My Trident once went into a high speed wobble when I was giving my speed-demon daughter a ride, and the problem was finally found when I changed fork oil, and one side didn't have any.