Yes, the bike in question is in my signature. The bottom bracket is not the problem. I swapped out the old crankset for the Shimano 105 5800 cranks. It solved the problem. Completely. There was no rub or flex whatsoever. Unfortunately, it doesn't really fit the style of the bike. I'm not getting rid of it though. I also checked to see if my chainrings were true, and they are. I took apart the old cranks completely, cleaned them up as best as I could, wiped down the tapers, and WITH A TORQUE WRENCH, I tightened them on to 30 ft lbs. This improved the rubbing problem a bit, but they still rub. I also made sure that the cranks were on the least wobbly taper. It looks as if I should be looking for a wider derailleur. Are there any Suntour derailleurs with wider cages?
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