Ok, maybe I'm a minority here, but I think that the EA here is really asking for it with the Apollos.
What I might see (and be afraid of):
2 Battle:
--Mothership: 6 Lights, 2 Heavies.
1 Battle: -> 2 Raid -> 1 Raid + 2 Skirmish ->1 Raid + 1 Skirmish + 2 Patrol
-- 1 Light Cruiser, 1 Light Raider, 2 Scouts. (2 more HRs can be easily swapped in for the 1 CL, also).
1 Battle: 4 Light Raiders.
Net (if he can afford it): Mothership, 2 HR, 1 Light Cruiser, 2 Scouts, 11 LR.
Note what's key here: he can outsink you with ease. You won't be able to get to the Mothership before he barfs 'em all out, so don't even try. The Mothership will then probably go asteroid-diving (thanks, terrain) after that until it's ready to come out at game-end. He'll almost certainly have the scout advantage, and with a +6 initiative and a reroll, he'll get to choose which side of the board to start on. Note exactly that this above rationale is why the scouts are not on board the Mothership, I want that placement reroll.
with the above fleet, he will initiative sink with the 2 HR, the CL, scouts and the Mothership, leaving you having moved all your Hermes. At this point, the LRs wil pass -- sorta, maybe move behind terrain -- until the capital ships have moved, and the remaining ships will end up at range 31 to the Battle-level ships, pointed just over their shoulder.
Next turn, they will sink with the heavy ships again, forcing the Hermes to move to contact range. Then, almost to a man, they will all burst forward with an All Power to Engines. That'll move them 21 inches forward. This will be your one good shot, use it well. but even that isn't promising:
2 x 8 Flash Missiles (from the Appollos) -- CAF -- is 7 hits, dodge, say 3 (I'm giving you the benefit of the doubt here, even!) plus one critical for 8:8 + DD Critical, say, a 2:2 for 4:4 -- 11:11 after the GEG.
Notice you've killed .... nothing. The Omega might get a shot at something with its beam -- that's probably your best weapon right here -- but I'm not guaranteeing anything. At best, you'll kill 1 and cripple 1 light raider.
Now, the LRs will spend one more turn hunting -- (still using those beautiful HRs as initiative sinks in the back row ... although the Scouts may move to within scouting range at this point) and killing the Hermes initiative sinks. That should take 2 turns, and kill off another ... say 2 LRs, the days of CAF are over. He'll have 7 or so left.
(For example, 1 LR is looking for 3's on a beam. That's just over 2 hits per. With 9 LRs, you'll get about 18 precise hits. That's 18:18 and 6 criticals -- 7.2:12.0 or so additional -- for 25:31 or so per turn. That's 2-3 dead Hermes per turn.)
At this point, the Mothership and the 2 scouts can sink out your remaining vessels, and the Omegas and Apollos, with the maneuver of the Raiders, will be lucky if they ever see much of anything in F arc again. It's probably safe to commit the Light Cruiser at this point, and, if you can guarantee that the one Apollo can't get a shot at an HR, you can charge with it (all power ... of course!) as well. This will get the heavy firepower into the fight, safely, that the taking down of Hull 6 requires. Using the CL beams to kill the still-likely living EA fighters is also commendable.
The real problem is side coverage against the LR's. They really have Whitestar-itis. The move to a weak arc and light things up. The better responses usually involve lots of firepower in a few isolated systems that have arcs to each side. The Chronos might be a more compelling answer, and, if your fleet list allows, so might be Artemis frigates and Rail Hyperions.