Actually, the situation was a bit different - and is now resolved, but will note it here in case it is of value to others.
Ioncube was installed properly on the new server, but part of the old site restoration included a php.ini file in the root directory which included a path to where ioncube was installed on the old server - and which was not found on the new server. Once I renamed the php.ini file, the pages found the new server's ioncube installation without problem.