I'm lucky in the sense that our track will let me go almost any place I'd like to go. That being said, I'm not interested in dying any time soon, either. I haven't shot at a track that wouldn't let you go as far as the 60 foot lights, but I suppose limiting it to the tree makes it easier for them to keep track of you. My preferred location for bikes is between the tree and the starting line, much like your first image. This keeps their extremely bright headlights from messing with the autofocus quite so much, which happens far too often to me with bikes and sports compacts.
My preferred location for cars is usually between the tree and the 60 foot lights. It all depends on the lens and the car. If the car really carries the front wheels a long distance, like I expect this weekend, then I like being farther out. Most cars don't keep raising them up very far out and I can catch them from the tree.
I'd suggest letting the track crew get to know your shooting behavior for a while. When they are convinced that you don't take chances and don't interfere with the races, then they MIGHT loosen the reigns on you a little. If you plan to keep doing this, then a relationship with the track crew is essential.