So how can you get good at thinking this broadly about voicings on the fly? Try this visualization exercise. The hollow noteheads represent the notes of a diminished 7th chord. The filled-in noteheads are the roots of the related dominants, and the notes that make up the corresponding 6th chord voicings. And yes, altogether these are the notes of the diminished scale that correspond to this diminished 7th chord.

Examples

One :: Two :: Three :: Four :: Five :: Six :: Seven :: Eight :: Nine :: Ten :: Eleven