Sometimes nothing else works and you just have to take the one-in-a-million longshot silly option.
If your GM is paying attention, hopefully they'll realise that this is your last gasp, and pull something dramatic out of the hat for you.
Hopefully.
Commentary by memnarch (who has not seen the movie)
Hah, well that'd be one way to short everything out one last time! And interestingly, it looks like BB-8's head is attached on a pole of some kind to the body. Maybe that's just a feature of being in the droid-seat of the X-wing? I would have thought the head would still just be magnetically attached. Or perhaps it just looks like the head part was launched at the same fuse panel? If it's a different part that's breaking, that could make more sense.
I'm not sure how this would have been taken in the movie, but I think here it's a good bit of minor levity. Assuming BB-8's perfectly fine and that there's not an immediate reason to be sad or disappointed anyway. Sure, it's a little silly of a resolution, but it's obviously a key part of the movie so far, so having a brief moment of success before the inevitable downward twist would be good. I think this movie came out around the same time as the MCU started really increasing the amount of bathos used in that series, so it'd make sense from that side of things as well.
Transcript
[SFX]: Pow! {the last surface cannon of the Fulminatrix fires at Allan’s X-wing}
Allan: I fly straight at the gun placement!
[SFX]: Pow! Pow!
C-3PO: That wasn’t a serious suggestion. BB-8! Do something!
BB-8: I ram my dome directly into the fuse panel!
[SFX]: Smash! Fzzztt!!
GM: That’s using your head. Mechanic roll at -5.
[SFX]: Ram!
BB-8: 20!
[SFX]: zzzzt! kzzzzt!
[SFX]: ping! {the weapons display comes back}
GM: Weapons are back online!
Allan: I ignore them! I’m gonna sacrifice myself and be a hero!
[SFX]: Kzzzzt!
BB-8: Can I fire the weapons?
[SFX]: Zzzt! Krackle!
GM: Uh, yes.
[SFX]: Pow! Pow! Pow!
[SFX]: Kaboom! {X-wing fire destroys the gun placement}
GM: The gun is destroyed! You fly through the fireball and emerge unscatched.
Allan: Aww...