Coil switching is the answer. I could be wrong, but I think Aeroplane was recorded during Flea's Jazz Bass phase so you are looking for the sound of single coils. Wire your Barts with 3 way toggle switches so each pickup will have series/single/parallel and you're good to go. Your Barts have tons of character baked in.
Alternatively, you could get Nordstrand Big Singles in that size.
Or, just get a passive jazz like Flea used!
Fuzzrocious Club #194
Brubaker Brute Squad #18
Spector Club #224 (USA NS-5MM, NS-2J)