What we do is to back up the staging DB, overwrite it with the current production DB, then run the necessary migrations on stage to get the schema up-to-date.
This has a couple of side benefits:
- "Dry" run of the migrations you'll eventually need to run in production anyway
- Using real production data in staging/QA (as long as you're allowed to) can uncover some edge cases you wouldn't have accounted for using fixtures or manual prepopulation.