How to design the end of a race game such that over-rolls do not break the logic of the game?
Is there any way to design the end of the track such that over-rolls do not lead to any confusion?


Write "If your roll is enough to move up to or past the end, you win. If you roll 5 when you're 3 spaces from the end, that counts as winning." on the board, or in the game rules, or even on the end tile itself (with slightly different phrasing).

Designing the end of the track differently is only one means to communicating the rules. There are other ways, and just stating it outright is probably the clearest way.