They filter out fast games (bullet and faster) and moves where one has less than 30 seconds total time to make the move. They say this is to avoid capturing "random moves" in time trouble

It's interesting, because IMHO the moves that humans make when in time trouble (which intuitively look decent but have unforeseen consequences) would be the exact thing that you would want to capture for a human-like opponent that makes human-like suboptimal moves.

We did not, we removed bullet games because they tend to be more random, and also did some filtering of the other games to remove moves made with low amounts of time remaining for the same reason. But the models don't know about different time controls right now.