I cuurently work for the US Department of Justice and planned on staying with them and becoming a lawyer..entry level states school doesn't have to be ABA if you are able to sit for the bar in ANY jurisdiction. I would have to pass the bar in CA but don't know how competitive I would be..
If you are in California, then you are in luck, if you can pass the Baby Bar, you'll be well on your way. If you work at the DOJ, one of your best resources would be.... human resources! Ask an HR guy how he feels about non-accredited schools. I'm in a similar boat as you, in that I am a paralegal, so I have the legal experience, just not the Bar Card.
Ultimately, I chose to go to a traditional school with ABA accreditation. The low passage rates of the DL schools scared me off. On the otherhand, I received my BA from an online program at UMass, so I'm not one of those anti-online zealots. But I think that since you already know where you want to end up, you should ask them directly about their feelings on it.
As for your LL.M question, you should ask St. Thomas University directly.