Bobby,
What you want is best done with a few smart campaigns. You could insert these inside the Engagement program or just put them in a regular Program.
1. Send Campaign Email 1
2. Send Campaign Email 2 (Listens for Campaign is Requested)
3 Send Campaign Email 3 (Listens for Campaign is Requested)
4. Trigger Campaign: listens for CTA miss (NOT WAS CLICKED) and then pushes that lead into Email 2 or 3. (Remove from Flow, Call Campaign).
Your interesting moments can be in a separate listen campaign...although I usually make these generic and not tied to specific Programs.
Another way is to use Streams to take advantage of the transition Rules:
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Stream 1: has all 3 emails, does whatever it is supposed to do each day.
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Stream 2: pulls in leads that match that criteria you mentioned
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Stream 3: pulls in leads that received Stream 2, but did what you mentioned, sends email 3.
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Separate campaigns must listen for the interesting moments.