But I am sorry to have to bear bad news.
It is unlikely you will be able to upgrade this discharge. For a few reasons
First, when a commander is presented with a Sailor who is eligible for separation based on more than one basis (as in your case) the commander gets to decide which basis to select. The JAG you spoke with, I fear, was confused, or perhaps just did not understand the law.
So if they processed you for the conviction (if that is what you were served notice for)? Then it is unlikely you can challenge that and win.
Had the processed you for one thing, but discharged on another? For example, had they given you notice they were processing for the treatment failure but actually used the conviction as a basis? Then you could challenge the separation.
But if they gave you notice, and you had the DUI (it sounds like more then one of them)? They can process you for that. The fact you reported it, or that it was old, or that you went to mast does not prevent the commander from using that as a basis.
The other problem you face is that you received an honorable discharge
and both basis can award an honorable discharge...so even if they used the wrong basis, it is unlikely you would be able to upgrade to an honorable.
I am sorry to have to bear bad news.