Hello Kendall, a nice problem here: Whether to keep it as is, or turning it into a "proper" 1163 or 11063 - I mean the kind of problems most of us would like to have, if funding allows it!
First, even TH Customer Service dept. for some older models may not have all the right items, so it might be it came back like this. Or it may - more likely IMHO - have gone there already in this config and they simply serviced the movement. After all we're talking about a 30-yr old model (dial & hands) as a minimum, and much older, maybe even more than 40, for case and bracelet. So the TH service was unlikely to have been the first for this.

Surely a non-original combination like this affects the value, as both a correct 1163 and a 11063 would be worth more.
I am no real Autavia expert and many more knowledgeable forum colleagues will provide their own advice, but here is my contribution for what it's worth:
1. The bezel goes with the case, as they have very slightly different dimensions and are not interchangeable. So it's a 1163 bezel - either original or aftermarket, hard to say.
2. The bracelet, especially if marked Gay Freres on the clasp, is worth a little fortune by itself and is always a little slack and stretched. So hold it dear.
3. If I were you, I'd make it a true Autavia by going either the 1163 or the 11063 way. This surely if you can afford it or you're willing to sacrifice the "wrong" pieces once you have chosen which you want. Try making yourself an Autavia culture here on OtD and at Alex's excellent tutorial at www.heuerautavia.com. - and decide which you like more.
Based on what you have on hand, if you were offered both the (larger) 11063 case and the 1163, consider that the GF bracelet of yours won't fit the other case, as it's got 21-mm lugs instead of 20mm as this one. So going 1163 can be easier, a new dial and set of hands and that's it. Many here will tell you that if you just have to settle for an automatic Autavia, the earliest one i.e. the 1163 is the one. But it's your own taste, and personally I like both the same.

Hope this can help you somehow.
Cheers
Fabrizio