I normally would not recommend such an action but;
If you have in-writing all documents that prove ADT is in the wrong, then hire a lawyer and sue for "Mental Anguish".
First get in writing their response that you cannot terminate without paying. Then, find a lawyer that works on commission (usually 50% of the winnings). That way, they will work for their money, and you won't be out any more. A good sleezbag will tie them up in enough litigation, that they will settle to cut their costs.
Remember, even maggots have their purpose in society.
I would first try to settle the matter through normal channels. Take names, document everything, ask for their claims "in-writing". You should be able to escalate your problem to the proper persons in ADT to clear up the matter.
If you decide to sue, get documentation from others as well. The lawyer will be glad to handle a classs action suit and make more money in the process.
This response is no joke. Good luck. Sorry to hear of your anguish.