I wouldn't get hung up on your middle name not appearing on the actual BP. Mine certainly dosen't and in fact my first name gets cut-off as well so even I would fail a strict 'full name must be on the boarding pass' test.

Yes I would try a chargeback with your CC.

Which country are you based in as you could try their airline regulator as well as the Italian one? I'd also try the Greek regulator as well since that is where your flight was from.

Does one of your national newspapers have a consumer or travel writer? if so contact them. They may not intervene on your behalf but they could write something on airlines acting in bad faith in this way. They hate being embarrassed in this way.