If there's any extra thread on the adjustable cup, you can put a spacer (same spacer as is used behind afreewheel or Sturmey Archer cog) behind the fixed cup.
+1. I think this is the simplest, most cost-efficient approach. Sounds like you probably just need to move the crankset ~1-2mm out from the frame to give the chain enough clearance to avoid rubbing the large ring. The spacers come in different thicknesses (1mm, 1.5mm, 2mm, etc.). Before heading to the LBS, you can do a test run without the spacer by loosening the fixed cup, then re-adjust the adjustable cup, and measure the gap between the BB shell and fixed cup to determine the correct size spacer required.
Considering the drop from the middle to small ring, I'm surprised you aren't experiencing the same issue with the small ring x 2nd cog. Chain rub isn't an issue in the smallest ring?