It's not reverse flow in this case, polarity shouldn't make a difference since it's just a magnetic pull. The problem OP is facing is that the coil is just a magnet pulling the projectile towards the center. At t=0, the projectile gains a ton of momentum rushing towards the coil, by the time it gets there the magnetic force has dropped a ton since the voltage of the caps has dropped. But there's still a little bit. Once the projectile gets past the coil, the magnetic field is now pulling back on the projectile, slowing it down. Since the voltage is much lower from when it started, it won't be an equal force, but it'll slow it down none the less.

There will certainly be a ringing after the coil dies down, but I don't think that's the source of OP's problem. Good point though, I recommended IGBT'S for switching the coil off and I didn't think of the flyback current on turn off. OP, look at guides to put a clamping/flyback diode across the IGBT. A 1N7007 should be fine. You can buy like 100 of them on Amazon for like $10. A great thing to keep in the electronics drawer too.