Most Shakespeare has been staged in different periods, but I haven't seen very many musicals taken out of their periods. I don't think Rent counts because though La Boheme was staged in a different period, the musical has been staged consistently in the same period throughout its existence, which is what a believe the original post was about. And I don't see how the Sweeney revival was in a different period (sort of hard to tell from the minimalist sets).
Keep your morals, I don't have time. Keep your lovers, I'm changing mine!
-The Likes of Us