Ah well, that's probably saved me some frustration. Thanks for that. It'll just be dismal work with the hated material.
To reduce the dismalness:
Start with 220 on your sanding beam. A couple of swipes right down the string path. That will show you right away if there are any dips and where they are. The dips will be the shiny gaps in the sanded line. Just do the string paths; no need to sand the whole board with 220. Keep sanding on the string paths with the 220 until the shiny gaps are gone. It won't take long, because the 220 cuts quickly.
When the string paths are all nice 220 grit scratches, switch to 400 on the beam. Go over just the string paths with the 400, making sure that the string paths are all nice 400 grit scratches, with no gaps of 220 scratches.
When the string paths all look perfect, keep going with the 400 on the beam, but moving off of the string paths, sanding the spaces between the string paths. Go over the whole fingerboard surface with the 400 on the beam, but be very careful to always keep the beam aligned with the string path, whenever you are on the string path. Sanding with the beam off-angle to the string path can put in a fresh dip.
That finishes up the leveling. From there, move up to finer grits on a soft pad to bring the surface up to whatever level of shine you want. For most fingerboards, I do 800 paper, then Light Grey Scotchbrite, then White Scotchbrite. That'll bring most fingerboards up to a nice semi-gloss. Buffing with a soft cotton wheel for a higher shine.