Well, a planer is the perfect (but expensive) solution.
First, arrange to cut your fretboard so that the grain is at right angles to the future top, not flat-sawn with gran lines that parallel the top.
Barring a planer or hand planes and skill using them, you can make a flat sander. I made mine from an inexpensive 3/4" x 6" x 36" replacement marble window sill from one of the Big Box stores. To that I glued two (different grits)) cut-open 3x24 belt sander belts (grit side up, of course).