Reason I don't think there is a dual time line:
-when delorous flips and runs, she runs into William. Dolores is detected as out of her loop. when William gets to that border town place, some employee in costume approaches her and says she needs to come with him to get back to her loop(or something). William steps in and says she is with him.
So, either this disproves the loop, as the head guy of the behavior dept just finished with his weird personal interviews with her in present time, or the head behavior guy is also in the past, which he isn't because they show him all the time with old Anthony Hopkins.
Then old MiB is shown in same place/time as old Anthony Hopkins.
So, it appears one time has old AH, flipping out Dolores, and the only variation of head of programming are all with each other at one point or another.