No lawyer can give you a guess as to your chances at court-martial. I can't predict what a panel of jurors are going to do in a case in which I have not seen the evidence. I would recommend you contact a couple of lawyers on this forum, let them review the packet and advise you, and then decide what you want to do.
This post is for information purposes only and does not constitute legal advice, nor does it establish an attorney client relationship with Mr. Cassara.
The bottom line is that your chances at a court martial depend on your reasons for violating the off base liberty policy. If you have a legally valid reason then your chances are good. If you knew about the policy and just chose to blow it off then I think you know the answer to that. It also depends on whether or not the policy is punitive in nature. In order to answer this, I would have to know more about the policy.
A court martial is not for the faint of heart. If you choose to refuse NJP, rest assured you are likely looking at a court martial. Commanders rarely bluff about that. But you might get lucky. If you really want a court martial with the facts you just described, you better have a legally valid reason for not complying with the policy and assemble a good defense team to advocate for your rights.
THIS POST PROVIDES GENERAL GUIDANCE AND DOES NOT, IN ANY WAY, FORM AN ATTORNEY - CLIENT RELATIONSHIP WITH THE ORIGINAL POSTER.
Sometimes it is better to cut your losses and move forward. Nonjudicial punishment is a certain result for you. It may be distasteful, and you may believe that you don't deserve it. However the consequences of a finding of guilty at a court-martial can be much much more severe than the results of nonjudicial punishment. Those results could more your record for life.
Based upon the facts that you have provided, it does appear that you knowingly violated the policy or regulation. While I would agree that your rationale or motive may be relevant, you freely admit that you violated a policy knowing that it existed. By now you certainly understand that I voluntarily joining the military you surrender many of the civil liberties the rest of us have.
You can certainly feel free to directly contact attorneys on this forum. However based on what I've seen I recommend that you take the nonjudicial punishment and move forward.
Best of luck to you.