With a 7500 squawk and the pilot not verifying that the flight deck is secure after repeated requests (I didn't hear him ever say that it was) I'd definitely be experiencing a pucker-factor moment, too.
From the sound of the audio and the timing of the communications (see Sun Country's lack of response to ATC during the dead air), I'm guessing the equipment failure was on Sun Country's side.
Professionally handled by all, but the pilot's gotta be red-faced over that one.