How should I address a letter to the Adjutant General of the MS National Guard?

You should give at least 2 or 3 months for the conditional release to come back. I wouldn't send any letter before that time. Also keep a good log of the dates you have talk this with your chain of command, giving opportunity from squad leader to your company and/or battalion commander. This will give your letter a strong meaning on why you are writing to him and also show that you give your chain of command the opportunity to address the situation. If you do the letter, make it clear that you are in need of going AD, this probably would help.
I had a friend in the NG that wanted to go AD. After going thru the chain of command didn't got any help. The AG of PR had an open door policy, so he went to him directly, but keep in mind this was after he gave ta chance to his leadership. He stated that he needed to go active duty because of financial hardship. They approved the conditional release for him after a few weeks.
Hope this info helps, good luck.

Maybe i can help clear this up. The letter you are writing will eventually be read by the AG. But it goes threw many hands before it reaches him or her. Your packet has to go threw your COC first and everyone has to sign off on it. Your 1SG also has to write a letter as well. Once your packet has been put together it goes to BN then BDE if it makes it threw those stages it goes to state level (AG) after that you should be getting an answer. I'm in the process right now and its been about 2 months and mine made it to state last week..so now i wait! I've heard its pretty tough leaving the MS guard i wish you good luck

Go online and find the format to do a request memorandum. If you have the opportunity, you should ask the company admin to assist you. Make sure you have a subject line that is clear, then outline what you want and the reasons for it. Since the CoC told you to initiate, I would see if I could include him in the signature blocks.