I'd mixed a few of the ideas up, and this proposal fell out.
Vanilla Admirals I'd make a vanilla Admiral free. So each player gets one for his fleet. But make them only available in games of a certain size or above.
Patrol - None available, they have better things to be doing with their time
Skirmish - None available, they have better things to be doing with their time
Raid - Admiral with one Trait (think a Veteran Ship Captain)
Battle - Admiral with two Traits
War - Admiral with three Traits
Armageddon - Admiral with three Traits
The Admiral must be placed on the ship of highest PL, or on a ship with the Command +X trait.
The Admiral is located on the Bridge. Any critical hit to the Bridge location (6-1) has a chance of injuring the Admiral and his staff. On a roll of 5+ the Admiral is disabled for the remainder of the game (and is unavailable for the following campaign turn). The enemy scores half VPs for killing a ship of the same PL as the Admiral).
Should the Admirals vessel be captured, then there is a possibility of capturing the Admiral. On a roll of 5+ the Admiral has been successfully evacuated from the ship before he is captured. A captured Admiral scores double VPs for capturing a ship of the same PL.
Should the Admirals vessel be reduced to 0 crew (including by destroying it), then there is a possibility of killing the Admiral. On a roll of 5+ the Admiral has been successfully evacuated from the ship (and may be recovered after the battle in the same way as adrift hulls). A killed Admiral scores equal VPs for destroying a ship of the same PL.
Campaigns You'd get a free FAP to spend on Admirals (broken down as normal from the list above). For example, in a 10 Battle campaign, you could have a single Battle level Admiral, or two Raid level Admirals.
Admirals may be swapped between ships in the roster in the same way as fighters.
An Admiral may attempt to increase his traits. Not sure the best way to do this.
Should the original Admiral(s) be killed, a replacement commander may be requested from Homeworld. The new Admiral will be at Raid level (possessing one trait) and cost the same as a Raid level ship (12RR). The higher ranking Admirals are rare, and are too busy serving elsewhere.
Named Admirals would replace any vanilla admiral and you'd need to pay extra FAPs for.