Unless you're really very comfortable doing precision woodworking, I would let a pro you trust do it. You'll need more gear that just a sanding block and sandpaper - you would normally want to have a long high-precision straightedge, and you'll need to have an appropriate workstand to hold the instrument as well. This is all stuff that will be expensive if you're not regularly doing this kind of work. Just at a glance, the gear you mentioned at Stew-Mac looks like it will be upwards of $200 and that's without the other stuff that you will need.
You can check out a book like the Erlewine repair book to see what's involved in levelling the fretboard. He would probably rough the pits out with a scraper or file, the restore the radius using a sanding block. You start with rough grits which will cut more quickly, then switch to finer and finer grits until you get to the surface you desire. 400 or 800 is probably where you need to end up with sandpaper.
This is all more difficult with a through-body instrument as you have to deal with the body as well as fully supporting the neck. You'll probably want to pull the neck pickup, mask the body, etc.
I think it's normal for fretless basses to have a bit of a ramp in the nut area to make fingering in the low range easier, but don't know how many frets up that is extended. If you were to cut the fingerboard comletely level to the nut, you'll probably find that it's hard to finger the low range, even when the strings pull the neck into relief.
I'm all for people learning to do maintainance on their instruments, but if you haven't done this before or want to go through this first with a lesser bass, I really wouldn't start on your Alembic.