Thanks for the tip!
I've been working the the extension exercises in Ray Brown's Bass method and find I can play comfitably (and in tune) down to the Eb scale - i.e. third position (5th position in BG talk). This means it's feasible for me to play the 1st half of the solo without shifting.
I'm still exploring playing with 1-2-4 fingering all the way through as well.
I feel my intonation is better when I don't shift as much - especially at this speed!
Has anyone else got any thoughts?