Issue patching SQL Server 2016 to SP2 CU 15
Thanks to SqlWorldWide:

You will need to install SP2 first in order to apply any CU that was released after SP2.

Applying the base SP2 patch allowed me to then apply the CU 15 patch.
Being forced into the DBA role, I tried this CU on our test server which was at the same patch level and CU 15 worked fine, hence my confusion.