By a long slow process of trial and error, I think it's an amp problem.
At home I mostly plug into a laptop with headphones, which masks any tone pretty well. But, I also have a Crate BT50, which is what I played through after lowering the pickups. Sounds just like a Ripper should through that.
For gigs and band rehearsals I've got a Markbass CMD 121H combo. Played it through that tonight, and all the problems were back. Played it through the Crate when I got home to check, and it's still fine.
So ..... vintage bass, modern amp design, some kind of incompatibility?