you can pick up some medium/fine mesh sieves on amazon, i will do a two-pass filtering where i use the mesh sieve to filter out most of the grounds and then run it again through a regular coffee filter. this is basically the same as using a french press, but it's cheaper to reuse old quart containers you get from takeout/yogurt etc than buy a french press.

ideally, it would be easy to find a food-safe coffee filter with the permeability of a plain paper towel (which i have used before, it works fine, it is not ideal, it's almost certainly not "food safe" in that use but whatever).