Since level banding was introduced I've been finding that the fleet actions have been largely abandoned, I've played through several where I was the sole player. They are doable that way but the fun of a fleet action is having a dozen or two other players working together on objectives.
I don't know if the engine will permit this but a better alternative to level banding may be to allow each player to see/fight all enemies on their level. For example a level 11 would be fighting and taking damage from a lvl 11 Neg'var, while a Vice Admiral who is cooperating with the lvl11 would be fighting a level 61 opponent. The damage engine could register damage not as set numbers being subtracted but rather as percentages being subtracted.
Another way to improve participation would be to have the login screen designate X fleet action as being a featured action for 24 hours. An additional idea would be to have labeled scenes from fleet actions display on the right side of the character selection area instead of the image matching the name you've selected to play.