I think that Abyssal sites should be integrated into Faction Warfare.
How the system would work is that when a Capsuleer uses a filament for any of the normal Abyssal sites a chance for a conduit into a faction warfare system would exist. When the conduit into the faction warfare is activated a filament would pop up in the system where the conduit leads to allowing a faction war defense fleet or any other PvP to enter the site to fight with the incoming faction fighters.
These types of sites would be able to handle up to three battle cruiser sized ships in the fleet and would have to complete a Triglavian room prior to entering the conduit into the faction warfare conduit room.