Again, different service, different program, BUT:
A friend of mine applied for MECEP five times. (It's an annual board, so you can do the math.) Anyway, the year of his fifth try, he got NJP - IN GRADE. This wasn't when he was a junior enlisted, either - he was relatively seasoned.
Nevertheless, the board must have looked at the whole picture: His prior performance, his character, and his potential, as he was selected and is now a highly successful infantry officer. I think the key was his recommendations, which included a very, very good rec from the officer that gave him NJP.
You seem to be in the same situation - Outstanding sailor, who just had a one-time brain fart. It's okay, it happens...that's why we have NON-JUDICIAL punishment. (If they court-martialed us for every infraction, we would have more brig guards than trigger pullers!) I bet it would have been nice to get away with a slap on the wrist, but in some cases, a commander's hands are tied.
Bottom line: You'll never know until you try. APPLY! In the mean time, do everything you can to strengthen your package. I would even suggest getting a letter of recommendation from the officer that gave you Captain's Mast. My guess is that he would be more than happy to help you out - it would be "proof" that his non-judicial punishment worked...it corrected a minor problem, and you continued to drive on.