Something was suggested to me as an alternative to my initial block mounting design. Rather than a rail design I could use drawer rollers to allow for vertical movement. I think this will be a much cleaner design and will require less wood and will likely be more stable than the initial design.

The roller rails I bought consisted of a corner section as shown as well as a flush section. As pictured, I attached the corner roller rails to the back corners of the block, these will all be free moving. The other part of the roller will be screwed into wood and attached to the wall. This will allow the block apparatus to freely move up and down.

The corners of the lid needed to be pulled back a bit to allow for the lid for opening. I'll be trimming those down in the future.