As tends to happen, there’s a little preliminary work I have to do before I move forward. Basically, I’ve got to set a seperate “modifier” key for global shortcuts than I have for local ones. In the end, this will mean that global shortcuts are accessed with Ctrl Alt <hotkey> and local ones are accessed with Ctrl <hotkey>, for example. It’s a bit of extra work, but it will give us ~26 shortcuts to use in the global scope as well as the same number in each of the local scopes.
EDIT: The new modifier system went in fine, but adding the first of the Polling hotkeys brought a strange Polling bug to the surface: when you use the hotkey to open the Polling menu, it opens two of them instead, and one is always in a really weird spot.