sJonathan,
Sorry, I'm still working on some good examples, and I understand that you were just asking a question! ... no prob!

Yes, I was talking about inversions on the first point. The notes are just roots of the same diminished chord.
On your second question regarding Db, I would say no because the chord you are voicing (Db) is the same as the tonic
of the key you are playing in.... in other words the rule says to use the dominant of the chord, which is Ab, and Ab is
major in the key of Db, so you take the major third of Ab, which is C, to get the diminished family... so then you can
see that F, which is the major third of Db, is not in that family... that's why I believe that you can only use the major
third of the root chord when the dominant of the chord is minor is the key you are playing in..
i.e. In the key of Db:
If you are voicing Db (the tonic):
Ab is the dominant of Db, and Ab is major in the key of Db, so you CAN'T use the major third of Db to get the dim. family...
you have to use the normal (dominant-->3rd of dominant) method
If you are voicing Bb (the sixth of Db):
F is the dominant of Bb, and F is minor in the key of Db, so you CAN use the major third of Bb to get the dim. family...
the major third of Bb is D, which gives you the same diminished family as the (dominant-->3rd of dominant) method...
in other words... F is the dominant of Bb, F is minor in Db, so take the minor third of F, which is Ab... and you can see
that Ab diminished (Ab,B,D,F) contains the major third of Bb, or D... Ab diminished and D diminished are inversions of each
other, so they represent the same root notes to build the triads on ... see? ... the "major third of the root" thing is just
a shortcut to what Diverse what saying, depending on what chord you are voicing, and in what scale...
I hope I've cleared up my explanation... keep in mind that I could be totally wrong about all of this.... I'm not trying to teach it,
I'm just trying to see if other people think what I'm discovering is valid.... that's all... (or think I'm discovering)
Oh, and I apologize for making your head hurt!

HTH,
Eggs