That was a good idea. Ultimately, it just showed me that Sublime Text was unaware of any command being submitted. It looks like iTunes may have the bindings super-alt-1 and super-alt-2, and prevent those keypresses from getting through.
Strangely, although I don't see them in the Default Keybindings file, if I press ctrl-super-alt-1 or ctrl-super-alt-2, I get the desired outcome. I have no idea how this happened, but I don't have the energy to "fix" this thing.