I rode the st1300 for 3 yrs I don't have any wobble. Though some say have. It could be types, suspension, windscreen position, rear box, rear suspension set up , wheel balancing and roads. I seen some rider past 200 but they don't fishtail or wobble.
Before this what bike you ride? Accessories for this bike is as good as zero in sgp. You can try eBay.