Which filler?

[arizmanor]

I have just finished a project, but I have dropped a clanger... A part if this consists of a small ply box. The sides I made from decent birch (I think) 6mm ply which had a nice surface finish. The top and bottom, I used some rough 3mm ply - the sort which seems to inject splinters at the least provocation.

The problem is that having painted it (primer, undercoat and top gloss spirit paint), the grain is so coarse on the top and bottom that it really looks awful compared with the nice smooth sides.

So I want to fill the grain and repaint the assembly. I should like to ask what filler I might use - I could use something like Polyfiller, but I have no idea how it would stick to the existing top coat and remain in place and will blend in when painted again. Is there another sort of filler which I might use and make a reasonable job?