look up the youtube video 'How to Make a Flavour Essence for Soda Syrup and Cocktails' by Art of Drink. He basically runs through the same technique using a vacuum filter. He is making 'essences' for soda using high proof spirit but he says it would work with 40% vodka. I'm gonna try in next week with a coffee filter once I get my hands on some magnesium carbonate. if I remember this I'll post my findings for you here.
update. works terrifically. i stirred the mixture for 15min then poured it through a coffee filter. it takes like an hour to filter out. halfway through the filtering, i dumped the filtered product back through the filter to get it extra clear. once the fines of magnesium carbonate settle and they do a lot of the filtering, so apparently its good practice to send it back through.