Tried one more time to have a web export since I remembered I accidentally uploaded it with the renderer Forward+ instead of Compatability (which probably shouldn't affect the save code but I really wanted web to work). And yeah, no it didn't. The checkpoints work fine when you are in the game and the save system even works across levels, which is really what I was worried about. But the location glitch is the huge issue. While saving and resuming brings you to the same level in the web export, it spawns the player in a different location not even close to the checkpoint. The only way the entire thing would work fine was if you never quit to the menu, and that's not the kind of bug I want to let fly.

So yeah, download only. Better luck next time for me, I guess.