Mokka pots are one of my favorite brew methods but they’re super particular if you want a really stellar cup. Grind coarse, do not tamp, pull the heat ASAP when the pot starts to spit at the end and/or when the color of the brewed coffee starts to lighten and you’ll get a great brew.
I can’t imagine using a restrictive filter in there when just changing from coarse to fine grind or tamping affects extraction so much. I expect you’d have a much better result just filtering fines after the fact like you’re doing.
I usually don’t even pour all of the mokka pot brew into my cup, I leave the last bit with the most fines in the pot and just dump it. You can also let the coffee sit for a little bit (a minute or so) after pouring it into your cup and most of the fines will settle to the bottom.