For a moment, this confused me. So…you need to disable unintented caching on those other parts of your domain. Not APO itself. Hence, adding headers and Page Rules to those other parts of your domain.
Yes, unintended caching for non WordPress parts of the site is the main issue with subdirectories setup.
I suspect it’s the entire zone, so all subdomains as well?
Nope, APO is activated per domain, it will require separate plugin installation on a subdomain to work.
One thing I don’t recall or haven’t seen: Does APO ever do a “Purge Everything”? (purge all cache in that zone…all subdomains, all directories, etc.).
Yes it does, on theme change it will call Purge everything. Purging by hostname is only available for Biz and Ent plans, that’s why we do purge everything instead of purge by hostname (e.g. only on subdomain).