I can confirm that this is not related to the orientation of the lot: I made four new ones and shrinked them, but all had this problem.
But then I messed around some more and I came across something I find a good instant solution for now: Placing an object in the cars path "breaks" the normal function and the car will just pop up on the street without driving animation. When leaving however it will ignore the blocking object and drive away normally (if the object isn't right in front of it and there's enough space to play the animation).
Outcome of my research:
- Blocking object has to be at least one tile next to the portal, it doesn't work if they're on the same line.
- If there're at least six free tiles at the enter side the car will be placed there (if there're more the car will be placed where the portal is).
- If there're not six free tiles but at least three free tiles at the leave side the car will be placed there, sims can exit and re-enter the car as usual at that point.
- Same for the opposite direction.
This solution works for shared lots, just placing a subtle object like e.g. a little tin can (or some invisible object) onto the street and the downloaders won't have to move the car manually every time, while those who have Ofb+ and miss the animation can just delete it.