A "more final" finish can be done on canvas by brushing on a thin coat of CA glue.
Canvas seems to be more porous, and the glue helps fill those pores.
This allows you to achieve better results with finer abrasives.
Sand to your desired finish, to the point you think sanding further is doing no good.
Then brush on a thin, even coat of CA, let dry. Then go to finer grit and lightly sand. Don't sand so much that you're exposing open pores again, just enough that your sanding only the topcoat and not the canvas itself.
Take the process as far as you want. If 3000 grit sanding followed by a polish is your cup of tea, probably could stand to use a couple coats in between grit changes.
At least that's what has worked for me. This also works well for "denim micarta".