Firstly, thank you for your service. Second, I'm sorry our leaders get away with treating us vets like they do. For all the flag waving people and politicians do in this country, they really fail to honor the vets when it comes to what actually matters. The Fed has been repeatedly asked to change the classification or at least allow studies into the effectiveness of medical MJ and it's repeatedly stood on the side of pharma and police agencies rather than the good of the veterans.
That said, the La. medical law would only allow you to use a cannabinoid oil with all THC removed. You should be ok with the VA as there would be no tests results showing you use pot since it's THC free. This is a big issue as I understand it because a positive test can cause you to lose your VA assistance. If your main issue is aches and pains, then a La. Dr. would not be able to recommend you for the CBD oil. Additionally, the La. distribution chain is still being developed so it might be another year before it would be available to anyone. I'd keep an eye out though as the law was written for periodic review and adding of additional conditions.
I'd recommend that you speak with other vets in your area and see about getting more to speak out or get representation so that there is more pressure to allow the VA to investigate.
Also, this is advice from a non-professional so you'd want to verify accuracy with your VA Dr's and private Dr if you decide to go forward.
Good luck.