I play lefty and struggle to find a 6 string bass that I like. I know Schecter has a few, but they're loaded with EMG HZs. I already have one Schecter with HZs that is just collecting dust because to me they are terrible pups. I found a used Brice HXB-406 online, but don't know a lot about the brand. I've read good and bad about them.

A few people on this forum have them and they seem quite pleased with them. As for your present bass, almost every bassist seems to dislike EMG Hz pickups. But you can always swap them out for a good set of pickups. The difference in tone is often remarkable.
"Maybe this world is another planet's hell?" - Aldous Huxley
Never had a Brice, but have a Douglas (also from Rondo, I think the same factory) Hofner copy that I beat the living hell out of in a punk band in high school and it's still going strong.
Cry yourself to ash
I have a 6 string brice and I love it. Eventually I will swap out the electronics, but overall its a great bass for the price. Their QA used be horrendous, but they have improved over the years.

Check out their webpage--for not much more you can get one new I believe, but its been a while since I roamed their site.