Based on what i've seen up to now, watch is legit except for the movement.

The Autavia with 2nd execution dial with lower serial number i know is 532xx,
and this 53047 falls perfectly in the bis subs range.
The execution of dial is the last one, so it is for the handset.
About crown and pushers, they are replaced in my opinion, as it is for quite all the early Autavia.
But i think nobody would miss a nice watch because of the crown!

About the movement, i read somewhere that Heuer merged with Leonidas on 1964.
Also, during the 1964 the watch industry was obliged to print the T on the dial because of the new tritium regulation.
I saw the switch to Heuer Leonidas movements, casebacks and the T applied on the dial in the middle of the production of the 2nd exec. dial
(not necessarily all 3 in the same exact time!).
The fact that the movement is the only part later in the watch can't still proof anything, because it's later just for few months not for years (see the balance for example, with the 22 screws in rim)
So it's possible that it has been a very late production, or it can be that the movement has been replaced in the early days (haven't we seen so many early 1163 with cal. 12 inside, because of the problems of the early cal. 11?).

But far to be a fake, i leave this assumption to the masters of fakes (like MM, just not to mention anybody).