If you 'pull' the frets on this neck, I'd too suggest going back with some sort of lines: You'd really have to sand down past the fret routs which to me would be playing with fire taking that much wood out.
As for the lines, DON'T use any kind of plastic. Ideally, a similar wood to the rosewood would shrink and contract with the rosewood. Lots of guys use maple, stained to an 'in the neighborhood' color where you can see them.
Sonicus has a great idea: Just get a replacement fretless neck. Then you can save this one for resale (or if you change your mind down the road).
Everybody makes Jazz replacement pickups. If I were going active without going Alembic, I'd use EMG's. Very familiar tone, quiet as a tomb, and if you sing, they're great as they don't ground to the bridge so you cut way down on your chances of shocking yourself instead of the crowd.
I hate single coil buzz. If I'm going to listen to the radio, I use a radio instead of my axe. So I'd use stacked passive Jazz pickups, and several people make humbucking Jazz replacements where they are in two pieces under the traditional Jazz shell side by side. I know it's not quite that single coil tone completely, but I'll gladly trade out for the quiet. Lindy Fralin and more make that style.
It's my three-question test for any axe, regardless of price: if it 1) isn't quiet electronically, 2) won't stay in tune, and 3) can't paly in tune up and down the fingerboard, what's the point?
J o e y