Exercise #4 (1973), opening bar. This example stems from Road tapes, venue #2, not yet released at the time Brett wrote his response.
Call any vegetable (1971), opening of the solo. The A7 chord upon an A pedal is strongly present. This solo begins in A Mixolydian with a C# dominating, soon to move over to A Dorian with a C natural.
The Gumbo variations, opening. In his response Brett writes about the Gumbo variations: "this is simply the blues scale in G, not clearly Dorian or Mixolydian". I agree that this song is mingling Dorian and Mixolydian. The intro from above obviously has the accent upon Mixolydian, the only scale that supports a Mm7 upon its tonic. Also Andy Aledort is indicating G7 in the Hot rats guitar book.
Promiscuous, opening. Here an open tritone is used (staves 1 and 2: F#-C), making the overall D7 chord sound more dissonant than usual.
Red tubular lighter, section with in bar 4 an A7 chord in an A Mixolydian environment. This example stems from The Mothers 1970, not yet released at the time Brett wrote his response.
Mr. Clean with blues in G Mixolydian. The G7 chord is explicitly used during the first bar.
This example from "Moldred" got released in 2023. It does exactly what Brett is calling prohibited in his 2009 study, including the argument he's giving why this chord does not occur:
The arguments I've come across how Brett would try to explain this away go like saying it doesn't count because it isn't "modal", it's not Zappa's "modal style", it's not "written" music, it's not "pure" Mixolydian, it's not what I wrote my theory for ...
But should such questionable intellectual qualifications be relevant? We are here talking about music. What you're hearing here is a G7 chord in G Mixolydian, and its resolving too. When Brett's theory has a meaning to you then the effect this "Moldred" section should have is something like "that's odd, this sounds as Zappa doing something wrong". Now does it?