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Figured it out. In the registry, the "HKEY_CLASSES_ROOT\Applications\sublime_text.exe\shell" key had the (Default) value set to something along the lines of "this is an intentionally empty blank value" (no, I didn't copy the value before deleting it, but it was something to that effect). Yes, really - go figure. Deleting that made Sublime Text suddenly appear in the Open With... list of installed programs dialog box.