I believe Critical Miss has to be played on a just revealed attack card, so that would be a no go. Not sure about TTHL; what is the card text?...
TTHL - Play in response to any attack card. Rotate the card to its next lowest value
I guess the bigger question becomes, when can you use a card on an attack that has already been successfully done and placed on the damage stack?
I know Twist The Knife allows you to specifically go back and change any card already played even if it's from a few turns before. Can you do the same with TTHL/NST or any other action cards?