Moreover, that bait and switch tactic brings into question professional ethics and misconduct, which is venturing into the legal realm. This professor needs to honor his policy to the extent that it does not adversely affect students who took advantage of it; in other words, if he wants to change his policy for future exams, fine, but if anyone suffers as a result of his policy, it needs to be him.
Ask him to honor his policy for your exam. If he does not oblige, politely thank him for his time and walk straight over to the Dept Chair. Keep on walking uphill until you find someone that appreciates the issue at hand enough to rule in your favor.
You'll work this out to your satisfaction.