Besides Meletios Metaxakis, Met. Dorotheos (the one who co-authored the "To the Churches of Christ wherever they may be" encyclical and gave his Panagia to an Anglican minister) was a Freemason, Pat. Joachim III was a Freemason and it's likely Germanus V was a Freemason as well. Athengoras, Demetrios and Benedict of Jerusalem were Freemasons. I believe one of the Patriarchs of Alexandria in the 20th century was also a Freemason.
How do we know these people were Freemasons? Well for one the Grand Lodge of Greece openly admits they were on their website: https://grandlodge.gr/ if you look around with a translation program there's a webpage titled something "famous Greek Masons" or whatnot.
post scriptum: I remember reading one of the reasons why the Bulgarians separated from the EP was because of the rampant simony within the Phanar and also the Masonic infilitration, and this was in the 1880s