OP, I don't believe you. I've been working LP for 15 years. I think you knew what you were doing and did it on purpose.
The place to argue about criminal charges is in a court of law. If you did not intend to steal these items and it was indeed an accident, then plead not guilty and go to trial.
You have almost no hope of winning.
As for the admission statement, whether it was voluntary or not really doesn't matter at this point. The police, in more serious cases, use far more coercion than they used to get admissions and those stand up in court all the time. The observation of the LP agent coupled with the signed admission will almost certainly guarantee a conviction - and frankly, the observation and testimony of the LP agent WITHOUT the signed admission would almost certainly be enough to win a conviction as well.

