What is the obsession with Liberators? Sure, they may live forever, but you're not putting out much damage in that time.
Under concentrated fire a LABC may not live as long as a Liberator, but it'll put out an order of magnitude more damage in the time it's alive--which means it will take less damage because the other guy will die first.
There's this stigma on Discovery that police officers are supposed to be flying LFs and not actually hurting people except in large numbers. Why? They're often going against pirates who have gunboats.
Give the police forces a light gunboat of some kind--a patrol craft. Essentially the Disco versions of coast guard vessels--because the police in Disco are a whole lot more like the coast guard (interdicting smugglers, etc) than local police officers.