Audrey with the SCN pickups sounds killer.
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THIS best answers the OP's original request for a 'relatively inexpensive' solution.
For the OP - IME the SCNs and other Fender noiseless pickups can be somewhat 'polite' in tone and output. An Audere pre is easy to install, reasonably priced, and will wake your bass right up! It is the best bang for the buck you can do to your bass. There are those who prefer passive instruments, but I personally like active with a good quality onboard preamp.
It is pretty easy to spend $500 on an electronics setup for a 4 string bass. You don't need to in order to get great tone and gain.
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