“The local ultra-conservatives despise Kyrill since they consider him too friendly with the Roman Catholics or even a crypto-catholic.”
The Old Calendarists in Greece say the same thing about him, but they hate everyone so far as I can see. My cousins in Greece tell me that to the extent that the Church of Greece has a preference, its +Kyrill. I know the same is true for the Greek Orthodox Archdiocese of America and I assume with the Ecumenical Patriarch.
Kirill is likely to win, just check the number a votes he's got at the recent Bishop assembly. I think the variant that the clergy and laymen vote against him, not plausible.