Refilled the grain and had it looking better and smoother than before. Sprayed primer, for the most part it built pretty well but there is still a little bit of visible grain. Figured I might have to add more primer since wet sanding probably wasn't quite going to get it smooth.

But then the dowel it was hanging on broke and the back of the neck got all scratched up. That eliminated any possible indecision about respraying.

Will sand with 600 grit like the can suggests and get the whole thing as smooth as I can, aside from the neck which I'll sand down entirely to completely redo. Then hopefully another can of primer will get that last bit of visible grain smoothed out.