My information is slightly different, so I offer it.
He was baptised Johannes Chrysostomus Wolfgangus Theophilus Mozart
At its root, Amadeus comes from the third of his long line of middle names, Theophilus: a Greek name meaning ‘lover of God’ or ‘loved by God’. In its German form, it translates as ‘Gottlieb’ while in Latin, it becomes ‘Amadeus’.
During his lifetime, Mozart did sign some letters in mock Latin as ‘Wolfgangus Amadeus Mozartus’, adding ‘us’ to the end of each name that lacked it presumably to make all his names sound latin-ish. If we reject Mozartus as being a comic affectation of Mozart should we not also reject Amadeus as a comic affectation of Amade.
He also morphed his name it is said into Wolfgango Amadeo, which later became Wolfgang Amade from about 1777.
He signed his name ‘Wolfgang Amade Mozart on his marriage certificate so perhaps this is the more correct name - Amade, as you say.
It was deemed pretty normal to translate your name into other languages in Mozart’s day but I feel we really should use only the names appearing in official documents where possible, as we have seen it quickly becomes very messy if we dont, particularly if the man himself uses many alternates as Mozart appears to have done.
Later upon his death the magistrate registering his death in Vienna entered this into his records - Wolfgang Amadeus.
I suspect that the magistrate in Vienna did not have the benefit of knowing he was baptised Johannes Chrysostomus Wolfgangus Theophilus Mozart, and lacked the inclination to research it, and perhaps saw no problem using the name often given to Mozart of Amadeus, and Mozart was not around to correct the magistrate and set the record straight.
And after that it all collapsed when Amadeus became the usual and accepted name for Mozart in society.
So which should we use, his Birth name, his name upon death entered into the documents of his passing, translations in other languages, his preferred name, or the name that society has decreed he be called.
I do not feel confident enough with all the confusion to disagree with your contention, you seem to have good sources, but I feel things are too confused to completely agree with you on this topic of what Mozart was really called given the time that has elapsed since his death and the confusion of history.
I guess all we can deduce is, his parents liked Theophilus, he himself liked both Amade and Amadeo, and the public liked Amadeus.
Perhaps then like so many things, when asked what his real name was, the only answer that can be correct is, - it depends.
And for me, if the viennese magistrate who registered his death did it wrongly as that of the death of Wolfgang Amadeus instead of his correct name of Johannes Chrysostomus Wolfgangus Theophilus Mozart. then surely we can argue that Johannes Chrysostomus Wolfgangus Theophilus Mozart did not die, and he therefore lives on.