Aegean has since told me that some system tells them that my flight number is ineligible.

Apparently, the database has some errors.

A number of Aeroplan were affected by the same error and made made a stink. AC has initiated an investigation into the matter. They have determined that, indeed, the UA database seems to be amiss. How long it will take to get it ironed out I do not know. But there is hope. :-)