If it is in a battlegroup then it can spend focus to boost to get back to two dice with its powerful attack ability so it can still have a decent damage output even when crippled.
The firefly's gun is mostly unimpressive, its main use to me is the eleap which can be used to bypass high defense, stealth or things that prevent attacks. (As eleaps aren't attacks)
Best thing to do when its gun is crippled is to forfeit movement to aim and shoot one of your electrically immune models in the back to arc the eleap where you need it.
It's also easy enough to hit most heavies in the game aiming even with only one dice.
Also good to remember that even though the gun generates the eleap, it is not considered to create the damage and does not suffer the effects of the crippled system.
It also still has the ability to help out with stormcallers even when it only has one box left, as it is not tied to any systems.
Even with its gun crippled it can still benefit from manual reload ability and get 3 shots if needed. Its main targets are low arm infantry but with one dice for damage you will likely to struggle to break armour with pow 6 blasts. I mainly use Grenadiers jack marshaled to gunmages so with runeshots you can use Thunderbolt for its push effects. Even if they don't kill a model once crippled you still have the utility of the push on 3 aoe's. Great for clearing zones or pushing models out of shieldwall for other models to kill.
These are the jack I most often have crippled guns on a first hit. Again I often have these marshaled to gunmages for the rune shots. Luckily it has a high base RAT so it can often still hit its main target heavies even with one dice especially when aiming. You can then use your jack marshal boost for damage.
With two guns it's not often you will have to deal with a crippled Minuteman. They tend to be fire and forget missiles, and mainly go from fully healthy to destroyed in one turn. Flak field isn't tied to an arm so would still work.
Its gun is not its main selling point really. It can aim and try to hit I guess... I have never had much use out of its shooting, but it's not why I take one. For me they are for shieldguards, holding zones or slambots.
With his high RAT and good likelihood of rangers being in the list he can use the Runeshot types even with a crippled Gun arm. Allowing him to use thunderbolt to push a model out of a zone, make a model not count for LOS with shadow fire or hit a low DEF heavy to kill a nearby model with Trick shot (which would roll 2 dice damage as like eleap its not counted as a ranged attack damage roll)
And finally if in doubt you can always move it to a suitable location and destroy it to give your important models some cover!
I guess you could use these guys in a pinch?
(Not that many people use them...)
What do you do with your jacks once they are crippled?