I had a similar problem when building up my Heron. I couldn't get a Record thin fixed cup all the way in. I gave up after the wrench slipped and scratched the chainstay. A Nuovo Record thick cup BB went in with no trouble. BTW, the thin cup is marked 1.370. I think that it's a tolerance thing. The Campy cups were a bit oversize, Riv BB undersized. Or it might be that the BB shell needs to be chased and faced. Neither cup set had any trouble on my Taylor.
Leonard Bulger in snowy Ann Arbor