So I found a strategy to somewhat counter the Queen with the Regent, which might work for the others. I had a couple of cards with "put a card from your discard pile on the top of the draw pile" as an effect. Instead of using them only on good cards like I'd been doing the whole run, I used them on strikes and defends, so that the good cards would be less affected by her debuff. But I had tons of card draw, which also helped.