One way of handling this is implementing some sort of incoming crash warning message, which pops up on the message box if you’re going to crash, say, next turn.
There’s still issues, of course, like what happens when you enter from the wrong side, or what happens when you enter at an angle, or if the vehicle is too broad.
An elevator-like teleporter wouldn’t suffer from these problems, of course, since you can just enforce that the ‘elevator tiles’ only exist on one z-level at a time and just move everything in them when the elevator moves. Sadly, elevators wouldn’t really fit for bridges. Some parking garages, yes, regular buildings, yes, bridges or boats, no.
Vehicle portions being able to move up or down in z-levels is probably the option that best adapts to problems naturally. There’s still issues like entering from the wrong direction or grabbers that it doesn’t solve, tho the later are a problem the current vehicle system doesn’t solve when driving diagonally.