I think that in '87 Shimano still had the Uniglide freehub bodies around. Finding a replacement cassette for the old system is very, very difficult so IMO prior to a chainring overhaul, I'd go for a 7sp freehub replacement since 7sp casettes are easy to get. Or if you want to keep the original 6sp shifters, by using a spacer, you can use only 6 cogs from the newer cassettes. Of course, this will convey a redishing of the wheel and a respacing of the axle.