Thanks for the suggestions, Xavier and Brett. I was able to create the required objectClasses (posixAccount and inetOrgPerson) by specifying an array of Strings in the objectClass LDAPAttribute, as per Xavier's suggestion:
attrSet.add(new LDAPAttribute("objectclass", {"inetOrgPerson"," posixAccount"});
I tried a solution similar to Brett's suggestion before posting here, and it doesn't work. It seems the attributes must be created simultaneously.
Thanks again.