Well, with the FBI (I know you said "other" agencies) their big interest right now is linguistics, buiology, chemistry and engineering. Those degrees with fast track you.
In the other major agencies (USMS, ATF, Customs, USSS, etc) it is really a mix of backgrounds for those coming through the academies. There does tend to be an emphasis on those with LE and/or military experience.
I'd apply at graduation (or soon before). Go on with you life, as if you have nothing "burnign in the federal fires". Pursue all your career golas as if the fed apps that you have submitted do not exist. The procedure can be along one. It took almost a year and a half for me, getting a near perfect on the exam, military exp (2MOSs and ROTC) adn a BS. I had a guy in my academy that was in the process for almost 2 years.
The worst they can do is say "no"... all the while you are going on with your life, making yourself more marketable for the next time around (if necessary). An agency may say no, while another may hire you... if you are bettering yourself in the meantime, who cares!
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!