I know these are old posts but I recently purchased a 2012 ST 1300 with less than 8.000 miles. Got a deal and had it shipped from FL to TX.
I realized that it had been sitting somewhere longer than I expected. I've put many hours in this bike now and about $1,200 more in cash. It now runs fine. I'm impressed with its light handling and how it holds corner lines, (that may be the new Michelin GT4 tires) compared to my 08 FJR.
I have first hand experience with the high speed wobble. In 08 I had a ST 1300 and chased a VFR through the mountains above Santa Fe N.M. At 128 mph I cut the throttle and the wobble began. In a just few seconds the front forks/wheel slapped to the left and I high sided the bike. I bounced about 50 yards down a straight road and came tp a stop. I was amazed that I seemed to be OK. I crawled to the berm and laid down. My friends came along soon and assisted with the mess I'd created. My Olympia Jacket was torn and ripped but never did the armour get out of place. I had no cuts or scrapes. My face shield was ripped off when I landed face first. No head injuries either. My armored gloves were shredded with knuckles ground off almost alt the way through. In short, the gear saved my ass,... or maybe the riding pants did. I was checked out a local hospital and used a rental car to get to the airport.
I'm reading up on the Super Brace because I can't have another wobble related accident, ever! I've analyzed this crash many times and concluded that I contributed to the crash.
I believe that I had far too much weight on the rear of the bike for that speed and that it contributed to to the lift that speed causes with fairings on the bikes i.e heavy rear end allows more lift in front. This occured on the first generation Ventures, e.g. I'd get to about 105 mph and the front end didn't want to hold the road. Many old Harleys exhibited frame wobble. You can watch them on U-tube.
I've now been riding 57 years, Sometimes you learn the hard way. I later found out the owner's manual tells us not to ride over 80 mph while using the top box.
These wobble problems are complex (tire balance, swing arm alignment, steering head bearings, bad tire ) but one thing we can do cheap is to avoid overloading the back of the bike and keep speeds within OEM limits. Speed is fun but speed kills. Ride safe