I played my six with C-F top strings for many years, it's a fantastic way to tune a bass, especially if you play a lot of chords/triple stops. works very well with slap bass too, you can slap out chord patterns.
With this tuning my bass sounds like a classical guitar once you are up around the 11th fret on the top strings.
There are plain bass strings available from D'Addario for your F.
Cheers Garth