Ok.
I don't understand your question.
A small question. If each of the 3 F, G, and I chords were different. Would either the German or Italian chord be "7#5" or just a plain dominant??
But, I'll try to answer in this way. Just throw out all the German, French, and Italian stuff. Any chord can be approached... dang, this is complicated. German, French and Italian Aug 6s are in essence dominant chords that have the same tritone. Ab7 and D7 have the same tritone. These two chords are know as double tritones. All dominant chords have this, it's b5 sub or relative. Not only do both chords have the same 3rd and 7th, their roots are tritones. That's why they can sub for each other, b5 or dominant 7. Now throw out the fanciful German, French and Italian Aug 6s. It's not a big deal for guitar players, because we can't voice chords exactly like a piano player. Some rules apply and some don't. Mostly, this can be done effectively by ear. The problem will!!! (I learned it the hard way, long ago.) arise if you orchestrate for other instruments, especially horns and winds from the guitar, and some lousy fiddle players. There are many, many, many, pitfalls. I would advise orchestrating on paper and checking on the piano.
Most of the examples were advanced examples of direct modulation to the key of G via tritone. The first three examples were a fancy way to get to the dominant thru a tritone secondary dominant. (in C or Cm) None of the examples shown, produced a #5. The logic is the same, though. b5 and #5 are within the same whole tone scale. (a borrowed chord idea) Any chord can be approached from 1/2 step above or below, by tritone, by 4th or 5th by a plain dominant or altered dominant. (remember I look at diminished chords as diminished or altered dominants, depending on what I want or the voice leading.)
I sincerely hope this helped.
A lie goes around the world before the truth gets it's shoes on. (Mark Twain)