The best BattleCorps story during the Davion Civil War was
Raven, by Jason Schmetzer
The best BattleCorps story during the Marik Civil War was
The Top of the Scrap Heap by Jason Hardy, though that was in the Outworlds Alliance, and had nothing to do with the League.
The best BattleCorps story during the Star League Civil War was
The Dark Night of the Soul, by Christopher Purnell.
The best BattleCorps story during the Pentagon Civil War was
Fall From Glory by Randall N. Bills.
The best BattleCorps story set chronologically during the FedCom Civil War (imho) was "Fragments of History," by Philip A. Lee, though that's about a Goliath Scorpion Seeker, and has nothing to do with the Steiner-Davion siblings. Nor does "Ambrosia," by Steven Mohan, Jr., though that's a great romp through the Hanseatic League's bureaucracy. Of BattleCorps stories during the FCCW directly related to the FedCom fighting, I'd go with Blaine Lee Pardoe's "The Longest Road."