BB install problem

all I can think is that maybe the tubes of the chainstays come through the BB shell/lugs and sit a little proud of the inside of the shell and the new BB goes a little deeper than the old cups.

Does this sound right and reasonable? It would be nice to hear that it's a common occurrence

Yes it's common with old frames, since the BB was tapped on the assumption of a cup and cone BB with quite short threads. Your LBS will be able to chase and face it if they're any good.