OK. Next idea:
(1) Set the month names to be the possessive forms, e.g. "Iouníou", so they can be used normally in dates throughout the site. (2) Create thingies in the Template namespace that contain the nominative forms, e.g. [[Template:Nominative-Iouníou]] would contain "Ioúnios". (3) Whenever you need the nominative, instead of {{CURRENTMONTHNAME}} write {{Nominative-{{CURRENTMONTHNAME}}}}.
Putting variables in links or template names causes link table corruption. We should have left it disabled.
-- Tim Starling