When I go through the custom setup, I get to the connect to Directories option and it does not populate the domain that is currently configured (and working for Win10 workstations that are joined).
You're right in using Custom Settings, because Express Settings can't be used in this scenario.
Can anyone point me towards instructions on how I can Syncronize Authentication for this server with Azure AD without also turning this server into a DC?
One of the prerequisites for Active Directory communication is DNS.
Through DNS SRV records, non-domain joined devices can locate Domain Controllers.
For non-domain joined Azure AD Connect implementations you'll need to point to DNS records, servicing the DNS Forward Lookup Zones and Reverse Lookup Zones for the Active Directory domains and forests you want to synchronize objects with.