viscid relic
After playing a good bit with cards like DNA, and seeing a content creator have Burglar and throw out a random High Card hand as a discard and getting screwed, I think it'd be a good idea to add in a special notification warning the player that they will be locked in or locked out of playing that hand for future hands.
This is particularly for The Mouth. It is quite annoying to lose a really amazing DNA + Hologram run because you weren't fully paying attention to the Boss Blind and oops, you lose because you tried to duplicate a card and are stuck on a terrible High Card-only round.
Something like briefly graying out/preventing the play hand button, with a warning at the top like other warnings saying "You will be locked into playing [hand type] for this round!" to prevent players from accidentally playing a poor hand and losing their run because of it. Admittedly, this is a skill issue, and the player should have been paying attention to the boss blind, but it doesn't feel good to lose a great run to something like that.
This could very well be a mod instead, but figured I'd throw it here. I feel this works best as a default-enabled setting in the game settings.
TLDR: Add a special warning and a brief disabling-the-play-hand-button to ensure the player knows they will be locked into/out of that hand type for the round for The Mouth / The Eye (moreso The Mouth)