Hey, thanks for the welcome!
And since you asked......
I saw a 2 string, plasma-bodied Sandberg California for sale via a US agent on eBay ages ago (there is a wooden one here
http://www.youtube.com/watch?v=Qj1JGyhGKMw). I have owned a few Sandbergs, fantastic basses and I wish I still had my favourite one, but I thought this one almost looked "do-able" as a modification. I did some modding research on line and lots of planning, even got a quote to have one made ($ same as a 4 string) then I decided to have a go myself. I watched out for a bass to start from, ideally with a truss rod since I was not sure what the impact would be of the wood removal exercise on the neck (I have only had to slightly adjust the truss rod once so far, but we'll see). It needed to be a Precision of some sort for the pick up. Spent a bit more $ than I was going to spend (inevitably) and bought a used Squier P-Bass. Not my colour, blah blah blah, but a good place to start. So long story short.....
I removed neck, removed the spare tuning pegs, thought about removing frets, the new join to body etc, then just made a start re-profiling the neck. Lots of slow work, nibbling away at it, sneaking up on where I wanted it to be but making sure I did not go to far. I stopped short of going really skinny (let's face it, a 25mm nut is pretty narrow anyway, but it could still be a smidge more C rather than D shaped further up the neck) and I played it for various periods before nibbling the neck again. I didn't do a "final" finish on the neck until I was pretty happy. I also chose to leave the fret markers on the fret board for the 12th fret to save some grief filling the holes and refitting markers elsewhere. I think the result is OK. I re-profiled the neck evenly on both sides so I did re-place the markers on the side of the fretboard. This profile also meant that I could use the original mounting to the body (that was my measure for the width of the neck pocket). I filled the tuning peg holes with dowels (bought bigger dowels and then shaped them for fitting via some glue and a firm smack). For now the headstock has a temp finish on it to fit the overall look (the whole bass is only temp finished until it's time for the proper job, maybe....). The neck itself is danish oiled, which is the way I like it (might have to do the same to my Jazz one day).
Then to the body. I removed the bridge and did buy a set of "bullet" bridge pieces to replace it but thought I would leave that for the proper finish job at the end, once I was happy with the whole job. So I have "trimmed" a replacement standard bridge to use the central 3 screws, since the Squier one was pretty rubbish. I may leave this as it is as it helps the bass look fairly standard. I removed the white pickguard and routed the body to move the neck half of the standard pickup to a central position. I modded the Squier pickup to use just the E A half (that's how it's strung) and I took the opportunity to line the cavities (it was a bit buzzy). I purchased a pickguard blank and made a new black pickguard (had enough left over to make a Jazz one too). Then I used wood to fill the gap in the body where the new neck profile did not fill out the neck cavity. Again, this is unfinished now but has worked OK to this stage.
Simple! Actually, it did take a while, but not as long as you might think. And there are things I'll do differently next time. But I only used a little bravery and the tools in my garage (no, I am not a luthier, or a joiner). It's strung with some left over flatwound D'Addario Chromes to give it a proper Precision thump, and it does pretty well, for a Squier. Smooth and light to play, but still punchy. I think it'll need some vintage Fender pickups, maybe 62s, to give it a bit more at some stage, but I like it the way it is for now. And yep, jaws did drop on it's debut on stage.
Try playing a bass using only the E and A. You get used to it pretty quickly, but you do need to use all the frets. And of course octaves can be a challenge, but not an impossible one. It's a blast!