As you noted, removing people from the engagement program is clearly not a viable option, as you'd lose the reporting data that way. However, can you not exclude the people based on their email address (or reference them from a list) from the campaign flow that flips the status back to the normal state? I think that'd be a viable option to explore.
Should I Use Complete users on the Engagement program to keep them from getting more emails on that nurture?
What does the "Complete" action do? I can't find any links about the Complete Status on Engagement Programs.
I think Complete could be one of the statuses of the custom program channel that you're using for the engagement program (probably the success status step). If you've setup in place where-in the send campaigns (in-case you're using the nested default programs as the content offers in the stream) to filter out people if their program status is Complete, then it'd make sense to transition people you'd want to exclude from nurture emails to the Complete status as a work-around. But, I'd still prefer changing EP cadence to Paused state instead of relying on the program status alone.
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