I'd highly recommend the Partheni Boatyard on the north end of the island of Leros. It's part of Agmar Marine which also runs the Lakki marina in the main bay.
The boatyard is immediately next door to the airport - you can walk over for regular flights to Athens at €41 on Olympic Air..
They've got a 70 ton travel lift and a 55 ton crane and can easily handle your boat. The workers are highly skilled for anything you'd want.
Craig Briggs, SN68, Sangaris