I didn't much like the stock strings on my California TT-5 SL either, so I installed DR Fat Beams, which I've always liked on my G&L SB-2. Huge, huge improvement IMO. Balanced, thick, and aggressive, without being harsh at all. I also like Pure Blues, but on this bass I think I'm sold on Fat Beams.
I've been interested in all the comments about pickup height, because I had to adjust mine considerably to achieve decent string-to-string balance. The A string was getting completely buried in mix, whether practicing through headphones or with the live band, so I had to raise the bass side of the pickups relative to the treble side, and then lower them overall. I also had to lower the A string saddle a bit. I think J-bass pickups should have raised center poles, especially pickups for five-strings, and yet very few do. I assume it's a cost issue.