Any chance the rear hub was originally UniGlide? HyperGlide came out in 1989, and perhaps it had not "trickled down" to Exage by the time the OP's bike was put together. A UG hub would require a freehub body swap to use HG cassettes, which is pretty easy.
[MENTION=367511]JamesRL[/MENTION], a 39T inner ring can be installed on your Exage Sport crank instead of the 42T, if you want to drop your lowest gear a little more.