This sounds like a problem that wouldn't depend on any of that. Pretty much anything you do breaks the checkpoints in some way.
Here is repro for one version:
1) Start fresh in browser (chrome for example)
2) Play until you get the custom pogo, and chapter 2 & 3's checkpoints
3) Go back to the menu
Result: I don't know. Sometimes you don't have the custom pogo even if you got it, and you don't have checkpoint 3 or even 2.
Sometimes you get checkpoints 1, 2 and 4.
Sometimes you get all four.