Methods and apparatus for constructing refractory structures, e.g., glass furnace regenerator structures and/or glass furnace structures having walls formed of refractory block and buck stays externally supporting the walls are provided. Opposed pairs of supports are connected to at least a respective one of the vertically oriented buck stays with cross-support beams spanning the refractory structure between a respective pair of the supports. An overhead crane assembly is supported by the cross-support beams. In such a manner, refractory components of the refractory structure (e.g., refractory wall blocks and/or refractory checker bricks) may be installed using the overhead crane assembly.