Obtaining re-authorization for a Mac app store app purchased under a now defunct Apple ID

Some time ago I purchased an application from the Mac app store. The permission for this app has survived through at least one new Mac but has not made it to my latest one. In the interim I created a new email address and, at the advice of the Genius Bar, changed my Apple ID to the new email. However, the app appears to be permanently attached to this old ID which appears to be unusable and my new Apple ID does not work.

The software developer is no longer accessible. Is there any way to retrieve a new copy of the app for which I have already paid?

Thanks for any suggestions.