There really aren't that many law graduates/lawyers applying (many wouldn't pass the BI). 
You are right. The MOST COMPETITIVE will have LE and/or military experience, along with education. Graduate education is a benefit, but not a huge one. That same time spent getting military/LE experience would usually bemore beneficial. With that said, you should still have a chance. You will not necessarily be in the most competitive category, but I would still put in for the announcements.
I am not even going to bother with suggesting an agency. Don't get me wrong, I have opinions on all of them. However, (with almost 13 years as an 1811) my perception of an ideal job may be drastically different than yours.
We bring evil things to evil people, kicking in a door near you!
."In theory, there is no difference between theory and practice. But,
in practice, there is."
- Jan L.A. van de Snepscheut
"The difference between 'involvement' and 'commitment' is like
an eggs-and-ham breakfast: the chicken was 'involved' - the pig
was'committed'."
-unknown
Working on a PhD in CQB one doorway at a time.
When the wolf attacks, he will find not all who run with the flock are sheep!