Thanks for the chance to help. I am an attorney with over 12 years military law
Let me first say that if they are processing you for a general discharge? Consider yourself lucky. I would not do anything to jeopardize that...the commander could, for example, change his or her mind at any time and process you for an OTH discharge (other than honorable). That is far more common for a drug pop.
What I am telling you is that if you choose to press this, you may well get the commander to realize that they have not chosen the conventional path and they could, very well, change the process to an OTH.
Now...it is more work for an OTH...they have to give you a hearing and a lawyer to assist. But neither will present a significant problem for the commander.
So if I were in your shoes? I woud not press this.
All that said, you want to speed this up?
You can make the request to your chain of command. I would make the request to your SNCO and let them forward it up the chain. You can do this verbally, or be more formal and put it in writing
I suspect this may speed it up...but as I explain you may get more than you expected
It is also important to understand the commander has no obligation to "speed this up"...he or she can sit on this till the end of your enlistment if they so chose.
Now...I would not expect that to happen. It would be unprofessional...and I suspect the commanding general would not look kindly on it. But the truth is that there is no statute of limitations on processing for misconduct...so the commander can initiate at any time.
Now...a practical note
if you submitted a few weeks back? I bet you are out in a month or so.