I would start by doing a good old fashioned decarbinization of the engine. SeaFoam can be used, and they have pretty good instructions of how to do it on their website.
GM used to sell a product called Cleens. It was for decarbonization and worked really well. I don't know if it is still being sold. You want a product that is listed for decarbonizing via the induction system, i.e. sucking it in through the intake.
You are lucky in that the ST1100 doesn't have catalytic converters to worry about so you can be a little more aggressive with the concentration of your chosen decarbonizing fluid. In the old carbureted days we would give it a real good soaking while holding it at high RPM to blow all of the looser crap out the exhaust right away. Then, again at high RPM, flood it with the decarbonizing fluid until it stalled. This ensured that the inside of the cylinders, the pistons, the rings, the valves, everything had a good coat of decarbonizing fluid on it. Then you just let it sit and do its job. After letting it soak you fire it up and run it long enough for it stabilize, and then you take it on the road and give it hell to clean it out. Then you change the oil and filter.
Word of caution- follow the instructions for the product that you use as far as letting it sit goes. Some of these products would not dry out and harden so they could be left overnight or longer to eat away at the carbon. Others would possibly have detrimental effects if left sitting to long. All depends on what's in them I guess.
Doing this cost very little, is easy to do, won't hurt anything, and is not invasive. If it works fine. If it doesn't, you have lost the cost of a bottle of decarbinizing fluid- and the smoke show will keep the mosquitoes away from you.
As bdalameda stated, it can be surprising what decarbonizing can help.
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