I'd like add to that list with..
- Fortress of Lies and Masters of War (Post-Republic book, but it gives good impression how prefecture were dealing with being cut off.)
I'd second Wrangler's suggestion there.
I didn't mention either of these because while they're set in the Republic the major players are members of splinter groups (Swordsworn, former Steel Wolves, mercs, etc) or outsiders (Clan Wolf).
that said, they're both excellent books.
On a side note I recently played a Megamek campaign of the combined Swordsworn/Republic defense of New Aragon against the Cappies.
Lots of fun - especially using the light cav/hit and fade tactics of the Ghost Legion against the Cappies