Here's my take on a very-short-scale bass guitar. The secret that makes it work are the
Bajo Sexto strings. These are designed for a 25.5" scale, and are wound with phosphor bronze over a steel core, so they work fine with normal magnetic pickups. I found individual strings on clearance for less than $2 each from Guitar Center, and bought the fattest four-- low E, A, D, and G (0.092", 0.074', 0.050", 0.046")-- but a complete set is still less than $15. (I later changed the G to an 0.042" ball-end acoustic guitar string to get the tension and timbre to match the other strings better.)
After temporarily checking out the strings on an old acoustic guitar to make sure they worked okay, I started searching for a suitable (cheap!) electric guitar on Craigslist. It only took a few days to come up with some good possibilities. I wanted something with a Strat shape, but with a 3+3 headstock so it wouldn't look quite as goofy as a bass. I decided on a Dean Vendetta XM, which was in excellent condition and cost only $50.
I removed the saddles from the Vendetta's vibrato-style bridge and replaced them with saddles from an old bass guitar I had hanging around. (The saddles from the Vendetta worked nicely on the donor bass, so it's still playable, too!) Experimentation on the acoustic guitar showed that the bridge would need to be moved back to get proper intonation, and there wasn't quite enough adjustment on the Vendetta, so I removed the six bridge fulcrum screws and reinserted them so the front of the bridge bears against them. (This required removal of about 1/8" of wood from the cutout for the bridge in the body, which took about 5 minutes with a file.) The vibrato spring tree is screwed all the way in so the bridge is essentially locked down, since I didn't want to use the vibrato feature on the bass.
The Bajo Sexto strings have loop ends, so I inserted a short 8-32 screw through each loop before feeding the string up through the bridge. I used an extra nut as a spacer to get the fat portion of the string to sit on the saddle.
The pickups are standard guitar humbuckers having six pairs of pole pieces. I covered them with thin, clear plastic painted black on the back side, and attached to the top of the humbucker coil forms with double-sided carpet tape. There are no problems with string balance, probably due to the relatively large gap from strings to pole pieces.
The tuners are the original Vendetta equipment, and accept the strings nicely since the fattest strings are made with a smaller diameter at the end to fit through the hole in the tuner peg. I removed the two middle tuners and filled the holes with plastic hole plugs from Ace Hardware.
The most difficult part of the conversion was making the custom nut. I used aluminum, since I had it on hand, but filing the slots took quite a while. If I ever do this again, I'll spend a couple of extra bucks on some plastic to reduce the labor.
This thing sounds fantastic! The Bajo Sexto strings sound awesome, with no "tubbiness" or goofy harmonics. Slapping, thumping, popping, and picking all sound just like they should.