Ah! You are correct that it was the image itself having something done to it, and perhaps also that the keyframes aren’t razor sharp. After a lot of trial and error I just noticed that the path of the properly-functioning track isn’t a straight line, and it’s supposed to be. Apparently, when I made the middle keyframe, I also adjusted the image’s location a bit and didn’t realize that. This mistake just so happened to produce exactly the effect I was looking for, so I never realized it was caused by an error on my part.
So, I simply opened a calculator, mathed out the position difference between keyframe 1’s location and keyframe 2’s, and then applied the same difference to the movements of my copied track. Problem solved.
I appreciate the suggestions! I’m sure I’ll be back to sponge more knowledge in the future. Take care.