But he sounds older than that in the narration: "...the best present I ever would get"
You probably wouldn't come to that conclusion in your mid-50s.
Why not?
When it comes to Christmas presents, I would say definitively '...ever would get' at this point when reflecting back.
Christmas is about kids and for kids more than anything. I can't imagine any Christmas gift being better than the ones I got at a time when they meant the world, therefore I would have no problem speaking in the definitive.
I like that we're giving the Zapruder treatment to "A Christmas Story" though.
As far as setting...it wasn't 'set' in the time of the narrator's retelling. If it was, the film would revolve around an old man in a chair giving an oral story.
The narrative device of recollection doesn't mean the film is 'set' in the time of that recollection.
By that logic, 'The Wonder Years' is a story about a middle aged man set in the 1980's. It's not...it's about a kid growing up in the 1960's.