[greymule]

"No runner shall be removed from the base occupied to bat in the proper place except the batter-runner who has been taken off the base by the umpire as in (2) above."

You're right about the syntax, but in this case it doesn't matter which "to bat in the proper place" refers to, because either way the sentence is factually wrong. No runner is ever removed from a base to bat in his proper place, whether under (2) or otherwise. As soon as a condition is put on this statement, it becomes untrue.

Men can't flap their arms and fly. TRUE.
Men can't flap their arms and fly except men who eat peanut butter. FALSE.

No runner is ever removed from a base to bat in the proper place = TRUE.
No runner is ever removed from a base to bat in the proper place except [any true statement] = FALSE.

The sentence has many other problems, such as the fact that you can't remove a runner who has already been removed (no runner shall be removed from a base occupied . . . except a runner who has been taken off the base).

The batter-runner who has been taken off base by the umpire as in (2) above is not removed to bat in the proper place. He is removed because the defense appealed when he reached base after batting improperly. It has nothing to do with where he bats.

The statement can be rewritten as a corollary:

"The only runner who can be removed from a base occupied to bat in the proper place is the batter-runner who has been taken off the base by the umpire as in (2) above."

But this statement is false.

The more I look at this, the more I think it may the worst written rule in the book. Quite an achievement for its author.