This is just a personal preference, but I've removed pull requests from the project's automation. PRs can reference and automatically close/move issues. Issues are then the only type of card on the board.
Also interested by this.
@kwhinnery can you give more information on how you managed to do this ?
I'm not sure to understand how to do it when you say "PRs can reference and automatically close/move issues" but that's exactly what I'd like to achieve.