-50
The Republic becomes the Empire.
"[...] in the Old Republic. Before the dark times,
before the Empire."
This is a non sequitur.
Nothing Ben says necessarily means that HE was personally present for the birth of the Empire, or personally remembers it. He is just discussing a World That Was, that he may only have heard about from his trainer, as one of the dwindling followers of the Force. He could have been trained in the Jedi arts by a rogue Jedi long after the Jedi Knights had been ousted as official guardians.
It could have been generations of secretive, hermit-style heretical Jedi, who were always fighting on the side of the various oppositions to the Empire. Plus Ben could have been 120, and could have trained Anakin when he was already 60.
The Jedi Order is disbanded by the Emperor
"the Jedi Knights were the guardians of peace and justice
in the Old Republic. Before the dark times, before the Empire."
The Jedi are persecuted
?
Obi-wan flees in "exile" and assumes a new identity.
"I haven't gone by the name Obi-Wan since oh, before you were born."
Again, you're unconsciously subscribing to PT plot-points that were not necessarily part of the SW backstory. The Jedi Order could have been deposed generations earlier--they were no longer "guardians" of the established political order, but were instead outcasts and rogues, fighting on the side of Good. The whole Clone Wars business could very well have been (and I actually think WAS) entirely a post-Imperial course of events.
Yes Ben fought with Leia's father, and then had to go into exile at some point afterward, but that doesn't mean it all happened in one big, pat, tidy singularity as the PT would have it.
Remember, SW was supposed to be a sprawling, sweeping world of Mystery & Magic, with ancient histories and dark secrets. Only later did Georgie-poo decide to boil it all down to one narrow, obsessively focused domino chain.