Thanks for this, however it doesn’t appear to be complete. The custom capability is added, however the capabilities do not appear to be mapped to the core caps required by administrators (or any one else who is granted the capability) to edit published posts etc.
There should be at least 11 capabilities for the admin role.
*edit. adding all of the capabilities might not be necessary since they should be inherited.
It seems that when registering the CPT using MB the mapping of the capabilities are missing:
'map_meta_cap' => true,