The terminology doesn't make sense to me either, but I think I can see where the confusion came in -- the top three strings in the tuning being what you'd find in a standard C tuning (all 4ths, two whole steps down from EADG).
Anyway, I, like others in this thread, have a hard time seeing a regular P-bass neck accommodating such changes in tension, but MAYBE it's possible with the right strings (I mean, Michael Manring does crazy things with his Hyperbass, but I don't think even he's dropping all the strings at one time). I wouldn't want to try it with my bass, though.
If you need the low tuning with the one band and you want to use one bass, tuning to C-standard (C F Bb Eb) and dropping the low string to Bb when you need to seems the most logical choice -- the compromise with dropping one string a whole step won't be nearly as bad as dropping three of them a major third and the fourth a tritone! I don't know how hard it'll be for you to play your rock band stuff in the new tuning, though.
The only other option I see -- aside from a tuning I haven't thought of that would work for both bands -- is a second bass. You could start with a cheap, used P-bass. Over here, a decent Peavey or Squier can be found for the price of half a dozen sets of strings. Might not be as nice as your Fender, but you're negating a lot of your Fender's potential with the tuning compromise anyway.
Last edited by MarkA : 12-23-2012 at 12:54 PM.