I am not sure if this would work, buuuuuut, here's another idea:
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Change the stream to send on Tuesday at 3 PM
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Create another stream in that program with all of the same content
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Set that stream to send on Friday at 6 AM
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Create 2 Smart Campaigns in the Engagement Program that are batch, recurring
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Use the Member of Engagement Program is Filter with criteria of Stream is and choose the engagement program for both and then the first stream for one and the second stream for the second.
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Use the flow step of Change Engagement Program Stream to the opposite stream you picked in the filter.
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Schedule the one that moves people to the Friday Stream to run right after the Tuesday send.
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Schedule the one that moves people to the Tuesday Stream to run right after the Friday send.
You would probably want to try this out before you rolled with it. This is merely a thought....