Yes, you need the conversion kit and I've had the best luck with the UN54 cartridge BBs. So far I've converted 4 Schwinn BBs on 3 bikes (one was a tandem). On the first couple of attempts I tried traditional cup and spindle BB, but they do not work.

The big mystery was always which taper length to use. Each crankset seems just enough different that the 1-3mm difference in length can make a big difference. So be prepared to swap BB until you find the best spacing.

On this Super Sport I used a Phil Wood 119mm BB.



If I remember correctly, I used a 121mm UN54 on the Continental.



The Tandem was a real challenge. The rear cranks used two different conversion kits in order to achieve the best chainline on the timing chain and place the triple drive crank in the correct position. I believe it was a 118mm UN54 that finally worked.



On the captain's cranks I used a Nashbar 115mm cartridge BB.