I don't have any documentation prepared.
However, it seems to me that you could, if you wished.... You could start with the British Columbia model and then adapt it to the national purpose. You maintain, for example, the parity of gender. You maintain the same number of people per riding. It wasn't needed in the B.C. case because it was an overwhelming consensus, but if in fact decisions are made by vote, you have sort of a constitutional amendment type vote.
This is just me talking. You would probably only have one representative for every two ridings because I think 160 people, 170, is about as many as you can properly manage, but I might be wrong. You could try it with one per riding. In any event, you would get a very good representation of Canada with the same random selection. Of course, there's a self-selection part to it too.