...
How would you rule when your ball teed off of 6 at Olympia Fields is at rest and your tee shot on 7 then hits the ball you teed off on 6?
I would treat it just like I would imagine they treated it back in the day when they allowed stymies. Play both balls as they lie. Trying to determine where a ball was originally and replace it after it was hit is just another time waster in the rules.
I don't see how the chaos you describe would ensue by changing the rules to allow playing balls off both the 6th and 7th tees at Olympia Fields. The rules simply allow a club to make a local rule specifying exactly when shots can be played out of order at their course. The local rule at Olympia Fields simply says players are allowed to hit their tee shot on 6 followed by their tee shot on 7, and then proceed to play the remaining shot in the standard order.
Kalen makes a good point, but not for the reason I suspect he thinks. You are not going to take a provisional if you can see where your ball is so that you would be able to see your second shot hit your first shot. The point is that since both balls would be out of sight from where they were hit, you don't even know the second ball hit the first. Since the rules want you to replace the first in this case, you have no way of doing that, thereby making the replace the ball rule somewhat useless much of the time. Even when the balls can be seen, it might not even be noticed that one struck the other, so again replacing is not done when the rules would call for it.
What about players on parallel fairways have balls hitting each other mid flight.
It seems to me the simplest way to proceed is hit it find it and hit it again, ignoring chance collisions.