Well, that didn't take long. I managed to find a solution to the problem.
It comes down to the fact that SQL Developer doesn't supply a search base, and my LDAP server didn't have a default search base defined.
When I edited slapd.conf (the OpenLDAP config file) and added a "defaultsearchbase" parameter, and bounced the LDAP server, everything started to work.
I now have a working configuration with OpenLDAP and SQL Developer.
I'll mark this discussion as closed.