I think solenoids are the way forward - 300 rounds/min = 5/sec! You could set up a metal end stop for the solenoid to act as a tigger to light the muzzle flash LED's.
Making them work would just require a bi-stable multivibrator circuit with a beefy enough power transistor to handle the current, and then you're all set!
I'll email my father and see what he uses for model railway point actuators these days, he certainly used to have some pretty compact ones that may just be small enough if you took a few liberties with the spacing of the guns (or had a single solenoid to fire them both - I'm assuming that they'd fire sequntially to mimise recoil, tho?)
Sounds easy when you're sitting on your backside day dreaming about it, eh?

Tell you what, if you can make this work and I still have a job in 6 months time, I'll go ahead and try to make the r/c attack helicopter I was contemplating the other week!

Mart