You can create a batch campaign to transition people to the Stream 2 per below -
Smart Campaign SL filters -
1. Opened Email, add all the 7 emails used in the EP's stream 1 to the filter, and set the Min. Number of Times constraint to 3.
2. Member of Engagement Program <EP Name> is true, Stream = Stream 1
Filter Logic - ALL filters

It's worth noting that Marketo logs a single open email activity for a person-email combo, so this filter wouldn't let people who'd have opened the same email 3 or more times to qualify.
Smart Campaign Flow -
Change Engagement Program Stream to Stream 2

Schedule this batch campaign as a recurring batch campaign, set to run a few hours before EP cast (you may also set to run this more freequently, but ensure that you schedule it in a way so that it runs at least 1x before the EP cast, preferably just a few hours before of the cast).