Another issue with these replacement bbs is related to how such frames are constructed. Electroforged Schwinns have wide open bb shells so usually no problem there. Some other brands have the frame tubes (seat tube, down tube, chain stays) protruding into the bb shell and those defintely get in the way. The standard bearing cup is curved on the inside but the sealed bearing units are more squared off and have to go in the shell farther.
You may need to clean out the shell a bit to get the bearing holder to fit all the way in. Grinding off some of the protruding stays may work but too much grinding may ruin the frame.
You can always swap those 28tpi cranks for 24 tpi cranks to work with the sealed bbs. They won't be authentic Schwinn but then a sealed bb isn't either. If you are looking to make your bike ride better, sealed bb and a cro-molly crank may help along with aluminum rims, good tires, etc.
I bought a supply of 5/16" caged bearings that have 12 balls instead of the fewer 9 or 10 ball versions that all bike companies use oem. More balls is better. Those get put in each of my cruisers as I service them.