Machine vs. Other in Audience Segment Filters

Hello everyone!

I work with a freelance client with specific defined audience goals. I'm blocked with an issue within the current segment filters to ensure zero overlaps but want to see if there's anything I'm missing or if anyone has a suggestion for me.

Audience groups and qualifications

1: New or active (within 120 days as defined by "created_at")
This group is defined as someone who has other opened within 120 days OR machine opened BUT ALSO clicked within 120 days OR their "created_at" date is within 120 days.

2: Lapsed/Dormant
This group would be someone who has done a verifying action to confirm their "real" but those actions are older than 120 (they have other opened more than 120 days ago or machined opened AND clicked more than 120 days ago).

3: Inactive / Never engaged
This would ideally cover everyone else. They've never other opened but may have machine opened but never clicked. If they have never other opened, or machine opened but didn't click, and the created_at date is within 120 days, they'd be in the first group until that 121 day mark.

Challenges

1: Someone can have both a "last other opened" and "last machine opened" within different time frames.
2: The Braze segment filters allow for AND and OR statements but those groups must use all AND or OR statements. I can't define more complex "if this, then that" scenarios such as [created_at is more than 12 days] AND [[last other opened more than 120 days ago] OR [last machine opened AND clicked more than 120 days ago] OR [machine opened never]]. This is possible in Mailchimp and I'm fairly certain in other ESPs (combining and/or statements within larger and/or statements).
3: You can't have more than 1 segment that refers to another segment. (I can't define group 1, then define group 2 but also exclude group 1 if there's an overlap).

Any suggestions or recommendations on how to get these first two audience groups into a segment with zero overlap?