I have had my Spyder for over 5 yrs, I still also ride a 2 wheeler (BMW K1200).
I noticed the same twitchiness when I first got the Spyder, and while at a Spyder Rally I got the Laser alignment. WOW ! it was a totally different beast ! It tracks true and straight, no wandering no twitchiness.
Take your time getting used to the Spyder, spend some time learning how to ride it on quiet roads, and stay OFF the curvy roads for a while. If you continue to ride a 2 wheeler, you have to recalibrate the brain to steer it..... I go back and forth btwn my BMW and Spyder, and the first two turns getting out of the neighborhood gets me re-synced . The Spyder is a blast to ride, and very safe with the traction and brake control systems.