HUGE shout out for AC Guitars (
www.acguitars.co.uk) here, they truly are a proper custom bass builder.
Alan, the man behind them does everything, by hand, himself and he has a massive array of custom options and not relying on CNC machinery, he can tweak, nip and tuck to your hearts desire.
There's a big choice of shapes, 10 standard designs, including single cut and more traditional styles, plus he's happy to build anything from his discontinued designs.
Two headstock styles, angles, or paddle (think Fender) and headless options on most shapes, plus he'll pretty much build any scale length, I recently took delivery of a 26.5" six string bass, and he'd gone up to 35" and everything in between.
An insane amount of wood options, including acrylic impregnated and resin treated woods, ACG have been using these for years, the market is kind of catching up now.
Neck construction, neck joint, fingerboard options, blocks, binding etc, all possible as each instrument is build by hand, not by machine.
Lots of pickup options, from traditional sounding, to more modern, all customisable as they are hand wound per bass by Aaron Armstrong, plus there's the Multi Coil MC pickups too.
Finally, there's also a great choice for preamps too, all built by the legendary John East, including the ACG Filter preamps, which as far as I know are now only available WITH an ACG bass.
The limited options you mention are almost always down to the use of CNC in the build process, even the slightest tweak requires a new template which takes time and can add considerable cost to a one off build. These guys aren't building inferior basses, but they are offering less choice and therefore less chance of getting exactly what you want/need. This certainly is not the case with AC Guitars
Here's some examples of the range available, I don't think anyone could argue there isn't a lot of variety and customisation on show here...
Here's mine too...
Cheers,
Eude