I stumbled across a concept that is new to me, but just an extension of what Tomo was doing with the Mixolydian diatonic triad devices.
If you build chords using the notes of the F Lydian b7 scale you get the following triads
F, G, Adim, Bdim, Cm, Dm and Eb+ (I think)
If you play with those triads you can get some interesting out sounds. The sounds do not sound "good" but they also do not sound "bad" or too terribly wrong. They just sound "out."
If you add the seventh you get
F7, G7, A-7(b5), B-7(b5), CmM, D-7 and Eb+
(I'm not sure what the seventh of the Eb+ is called)
In any event, you get some cool alternatives to the Bb major scale diatonic triads that sound very "nice" compared to the more dissonant triads using the notes of the F Lydian b7 scale. It is a cool way to add some flavor.