I really like the current fin and the way it is worn - very naturally aged. But if you must refin it, I'd do what you like and something personal.
The PLEK machinery is used on Gibson custom shop stuff and on all Warwick basses and Framus guitars. I've only heard rapturous things about it (from players, manufacturers and in magazines) - the difference is supposed to be night and day and it does away with even the most resistant buzz prone "evil spots" on the fretboard. While the PLEK machine works, strings are kept on the bass under full tension. All you have to do is say how low you want the frets before the process starts.
Grear score btw!