The fact there are ranks going all the way up to Fleet Admiral in the SA and Director in the LSF more or less kills your "grunts" analogy. Unless it was intended to refer to the average SA pilot, rather than a member of Southern High Command.
Who are you going to get orders from? The Northern Navy High Command? Plus, unless the LSF was split as well, how can there be 2 LSF's? That would be like having 3 RMs or 15 Das Wildes. Even if the Northern High Command gave an order, why wouldn't their Southern counterparts know about it? The Fleet Admiral of the NA presumably has the same security clearance as Fleet Admiral Woolsey.
Hell, why would the LSF not know about a secret mission into their own facilities? That's like trying to go into the Pentagon on the USMC's clearance without knowledge of the CIA.
There could, at max, only be 2 Navy and 2 LSF factions, due to the north/south divisions. Unless you propose to make something like a whole string of Northern LSF- XXX Branch or Northern Navy- 4th Fleet or something.