I rubbed the "filler" coats with extrafine steel wool instead of sandpaper. Against the grain.
I've never had to wet the wood to raise the grain, though I do put a couple of coats of oil finish on it. The last grips I did, which were ebony, had three coats of oil finish rubbed down and a final coat.
Make sure to leave it dry completely per the instructions. It's hard to wait, believe me I know. But if you don't you are actually hindering yourself. The first grips I ever made, I didn't wait long enough and it seemed like it took 20 coats to fill the grain.
The final coat I do the same as you. Polish it with a soft cloth.