I will say that your slightly less random amendment (when a film is picked a second time it moves up) is a bit complicated for me. My proposal is that we'd put all the names in the virtual hopper and then maybe pick 500 or 1000 of them at random (if we got 40 ballots, we'd have upwards of 4000 entries). Then they'd be ranked by frequency. Positional tie-breakers within this group would be, of course, random draw.
Anyway, I'm on board.