What happened on 3rd down has nothing to do with anything when it comes to clock status. What caused the play to end is what does.
The summary one of my colleagues came up with is that for NFHS code, if any of the following 10 things happen during a play, the clock will start on the snap or when a free kick is legally touched:
a - the ball goes out of bounds
b - B or R is awarded a new series
c - either team is awarded a new series following a legal kick
d - the ball becomes dead behind either goal line
e - a legal or illegal forward pass is incomplete
f - a request for a charged, or radio/TV, timeout is granted
g - a period ends
h - a team attempts to consume time illegally
i - the penalty for a delay of game foul is accepted
j - a fair catch is made
If, as in the OP, NONE of these items occur during a down, the clock will next start on the ready for play.
Since the player who caught the muffed ball was not the player who gave the signal, this isn't officially a fair catch (even though the down ends as soon as he completed the catch). No major clock stopper means that we wind it up on the whistle.