Your formulation of "indistinguishable" was already invalidated on reddit.com/r/hpmor by a different objection to my hypothesis. When you lie, you leak information. That information just puts the situation into the 6-hour rule. This cuts off the rest of your reasoning below. It also shows how hard the 6-hour rule is to "fool," which in turn explains why it hasn't been figured out yet.

EDIT: Rewrote one sentence to put the normal 6-hour rule back.

EDIT: Basically, if all of the information Dumbledore can receive from Amelia Bones could logically come from her departing anywhere between time X and time Y, then the metadata available to Dumbledore is effectively that, "Amelia Bones came from anywhere between time X and time Y."

In short, the rule is that you cannot convey information more than 6 hours into the information's relative past, but that does not necessarily mean that you cannot go to a forbidden part of the past after learning it. It merely means that you cannot change your mind about doing so after learning it. Worth noting: if you plan on going to the past, and then receive some information from 6 hours in the future that changes your mind, you have conveyed information to the past. I'm not sure how that is handled, other than that the laws of the universe are structured as to never allow it to happen.

I suspect my actual formulation (not your slight misread of it) and yours come out to much the same.