How do I keep my player's movement consistent throughout different levels?

the issue here is where are you modifying the values? are you modifying them through a script or the character placed in the level? if you are then the changes will only be evident in that level. If you want to make the changes the same for any and all levels then go into the character blueprint and select the character movement component and make your changes there. by changing the source bp (characterbp), anytime you create a new copy of it it will also have the changed values as its default.