What can I use to strain gritty bloody mary mix? I like Zing Zang bloody mary mix, but it's very gritty with seasoning.  I like to pour it into a strainer to filter out the grit, but the mix is so thick that it takes forever to strain.  Not only that, it doesn't get all the grit.  A strainer with smaller holes would help keep out more grit, but the thickness of the mix would make it impossible.

I've thought of adding a cup of water to the mix to thin it out, but then I'd have to boil out the water and I don't know how to measure how much water I've boiled out nor do I know what effect boiling would have on the flavor of the bloody mary.

Any ideas?

Update: It's looking like my only option so far is to get a high-grade blender that I can use to pulverize a entire bottle of premade mix.
Line a salad spinner with cheese cloth or another lightweight cloth. Fill and spin.