Shadows can manage because of the unability to be boarded (same counts for Vorlons, those might lose though due to the effect of AA being useless against 2AD emines).
Shadow Scouts will not be viable. AP emines will do 33 damage in a single turn without help from elsewhere. A Stalker will NOT survive two turns of firing from Emines alone, fighters will do extra damage.....If we assume 10 missiles coming into contact with a single ship, that is going to be 10 damage in a single go. Totaling a ship also in a single turn. So after 3-5 turns a fleet made up of a scout with 2 Stalkers actually doesnt have too good a chance. Self repair will not be used for long, due to the damage is just enough to kill you in a single turn. :S. (and i have only used 20 crewed missiles out of 60, with a bit of luck, they might penetrate the shield and crit for extra damage....or not ^^).
So an Abbai fleet....40 Breaching pods and enough fighters and emines to make sure enough arrive. Even 4 might should be enough to kill a Bimiths troop complement (if im right about the fact of Gaim troops rolling twice and picking the preferable die). A Bimith could even be killed via the use of 10 crewed missiles, and the full use of the Gaim fleets emine complement. But of course if you manage to capture every single ship on the board, you are even able to circumvent the fact that Queen ships are worth double VP.......