i have encountered that problem before...
i would use the schwinn race and make a brass bushing...
i cut a thin strip the width of the race...
then wrap it around the fork tube... mark the over lap...
then cut it a little short...
make two or three as needed...
use a flat blade screwdriver to push your spacers in place...
just make sure the race is tight... like it had been pressed in place...
some hardware stores carry hobby metal...
thin sheets of brass, copper, and aluminum...
i have used 5/8in soft copper tubing as shims for handle bars that slip...
works great... the copper being soft will crush a little...
putting a tight grip on the handle bars...
oh...
almost forgot...
sometimes you can wrap a shim made from a pop can around a loose handlebar stem to tighten it up in the fork...
some bicycle parts just will not work together...
but that does not stop me from trying...
ponytailmike
mike