Hi,
I am happy to share some experience on solid body electric ukes.
For adjustable bridges see moongazer at
http://www.moongazermusic.com/bridges.html. You can live without it by using a thicker than normal bone saddle and filing it for the different compensation for the different strings, but the moongazer's adjustability is essential if you'd want to try different strings or tunings, and you will.
They also have pickups, but if you want to experiment with making your own, you can get the parts to make telecaster style pickups to your own custom measurements at Stewart Macdonald. If you start with one Telecaster pickup kit, you'll learn enough to go forward. To learn more, they also have a book called "Pickups...and the guitar became electric" or something like that. Tuners, wiring, jacks, fretwire, etc. are available at Stewart MacDonald. They also have acoustic kits, which would teach you most of what you'd need to know.
My opinion is that you are better off with a "neck through body" design if you can get straight vertical grain wood, rather than a joint where the neck meets the body. I think there is inherent advantage in sustain, which is desired in an electric, with one piece of good wood directly anchoring both ends of the strings.
My first few were this way with maple for the neck and spruce for the body sides. Even with the neck shaved thinner than I'd ever like, it was overkill. This led to an experiment with a six-string uketar of red cedar and no additional neck reinforcement, based on "Left Brain Lutherie" book that showed the biggest contributor to stiffness was the fretboard. Now after two years including camping and abuse, it's still as true as new. I've been including a single carbon insert in the ones I sell, mostly to be able to say it's there.
For fretboard, you can buy pre-slotted maple or rosewood or ebony guitar fretboards also from Stewart McDonald, then cut back from the far end (wider spacing) to get to the approximate scale length for your design -which needs to be 2 x the distance to the 12th fret that you'll use. The precision on this is the most important, and while you can get the correct fret spacing dimensions I wouldn't recommend trying unless you are confident you can get accuracy to a couple thousandths of an in
One important thing - it won't sound very much like a ukulele, more like an electric guitar played up the neck. With a high-G reentrant tuning you'll get some ukulele feel, but you can be open to what you can do with your amp, effects etc.
For example, mine are at
http://www.markvinsel.com/UKES.HTM
-Vinnie in Juneau