Belatedest answer ever: don't think of it as changing the past, think of it as establishing a causal link to an alternate version of the past that had you appear in a time machine (and obeys other constraints, depending on the time travel rules of the story).

It's nice to know that someone else thought of this stuff as well. Here's what led me to the same conclusion without reading any hard science.

I got really obsessed with Zeno's paradox a few months ago and managed to figure all of this out independently, using similar arguments to come to the same conclusion. Time is just change over space. There are lots of parallels between what the arguments made here and what Zeno said. It's not identical, but thinking of Zeno led me to tangents that led me to think of this article.

I also read some quote by Einstein in a letter to a friend after the death of a loved one, saying that the death/life distinction is weird because there are space configurations in which people who have already died still exist. That helped too.

Some of the stuff on this site also influenced my thought process: www.scottaaaronson.com/writings/ (Pancake is the best one.)

And lastly there's a thought experiment meant to "prove" that time exists independently of change which failed miserably once I thought about it so it influenced me to move in the opposite direction.

You have three universes, galaxies, planets, rooms, whatever, labelled A B and C. All motion in room A is set to stop every two years and once it's stopped it stays stopped for a year. All motion in room B is set to stop every three years and once it's stopped it stays stopped for a year. All motion in room C is set to stop every six years and once it's stopped it stays stopped for a year. Then, supposedly, when they all finish the sixth year and move on to the seventh year they would all "wake up" at the same time and be able to tell that time passed because their cycles relative to each other would have stopped.

My response was to say that it seemed like all time everywhere would stop if they all coincided (assuming that A B and C contained everything in all the universes), but also that the premises were flawed (assuming that A B and C did not contain everything) because a change in their cycles relative to each other was impossible without time existing in the interim. Their cycles cannot change relative to each other if one wishes to try to prove that time exists without change, the problem cheats by sneaking in a change disguised as the lack of change. The ultimate flaw in the problem which those problems stem from is presuming a larger existence outside of room A B and C in which the problem poser is posited and able to watch their relative cycles shift. I can't conceive of any way that would happen.

Lastly I thought that insofar as time might exist external to change it seems like an absolutely meaningless concept anyway. I don't care about "time", I care about material conditions and structures and the formations of certain things relative to me.