How can I fix a broken tailgun?

I would think the proper diameter of styrene rod would do, in that small scale. You could try to "dimple" the rod with a pin vice and a No. 80 bit to give it more of a three-dimensional appearance, if you have that tool. Or just try stretching sprue to the appropriate diameter, and use super glue to attach so you get a good, quick bond. Just be careful to keep air circulating around the turret as the glue dries so the super glue doesn't fog the clear plastic. 

I recently repaired a couple of gun barrels on a B-17 model I built for my dad when he was still alive.  He was in the USAAF in the 9th air force.   After he died I brought it home with me and 6 of the guns were broken.

 I used very small diameter brass rod.  Drill the old bits of barrel out with a pin vise and inserted the brass rods.  Just as easy as any other method and not much chance of breaking them again!