I'm converting a vintage Trek 720 hybrid to a singlespeed. It currently has a 112mm square taper BB and triple crank that I want to replace with an Ultegra 6500 crank and single chainring. The BB I have for this crank is a 6500 octalink 109.5mm one, but it seems to have no clearance against the chainstay. Is the simple fix to get a different octalink BB with a longer spindle?? Do they even make one that long?

Any input from someone who has done something similar would be appreciated! thanks