Well folks, I was generously offered the loan of a Dr. J Sparrow. It's great as an amp simulator, and I found it's influence on the sound of the bass was profound, actually 'overruling' pickup selections so it became the main determinator of the sound I was getting, but the overdrive just wasn't gritty enough.
So I eventually ordered a MojoMojo which cam this morning. I set everything at 12 o'clock and BANG! There's the sound I've been chasing. All three of the things I want but perhaps haven't been able to express at the start of this search:
(1) A distorted sound that 'growls' rather than 'fizzes' - not too bright and preserving the underlying tone rather than imposing all its won character.
(2) It gives a compressed sound dynamic but with changing tone, so the distorted sound gradually smooths to a clearer one (just like a good valve sound).
(3) It works well up the neck.
So I'm happy!