Supplying a fortress thousands of feet above the sea

How would heavy equipment and supplies reach the airborne island?

Use airships for the initial work, then install a crane and a shaft to lift loads from the sea below.

Captured airships are proposed for the initial work on the island. A crane and a shaft through the rock could then provide a more permanent lifting route. The base's value depends on sustaining it once the initial construction work is complete. The proposal leaves the load and engineering calculations open.