Ok I see what your doing with your book now. Cool.

I agree that the Amaddb6 sounds like a Fmaj. Although I think your missing the point of why I wrote it as such. That’s all. For every inversion there is a new chord produced, or I should say named. Probably not the best way to name the chord but you can use them as variables in a new equation. All I did was place these variables in the equation to make a harmonic minor cadence. This is perfectly ok. Actually Cmaj7#5/E to Fmaj7/A is an imperfect authentic cadence. It’s strange though cause of the augmented C major chord, and it’s not a dominant. Unorthodox, but as I explained the chords can be re-written, using the inversion as the root instead, to show what it really is or could be. It’s not wrong, especially if your talking about voicing the chords in such a way. In the original the cadence is in the bass, the Cmaj7#5 and Fmaj7 would be something a guitarist could play over it as an option. Yes it’s odd and unorthodox but hey what’s wrong with that. ;)