I was a bit confused at first during the tutorial, but once it "clicked" i had a lot of fun. The only issue I can really see is the Queen is quite powerful and the king felt highly situational. I'd spend a lot of time just shuffling the "deck" til i had 2 queens to speed past levels that didnt require kings. I noticed you've designed at least some of the levels with different paths that favor different card frequencies, and that was really smart!
One way to approach things with this mechanic: Perhaps instead of making the cards random, have a limited deck of each type of card, and the player can select them as they desire, but they are only a single use. Then tailor fit the levels to be solvable with only the cards alloted for that level. You could even have a bonus for having cards left over at the end of the level.
Regardless, I really enjoyed this game! Excellent work!