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.

Putting a resistor in circuit will increase the response time, but that will reduce the force acting on the projectile in the beginning. You would get the same effect by reducing the charge voltage on the caps. What you, err... OP, ideally wants is maximum current going through the coil in 0 amount of time (maximum magnetic force) but turn it off right when the projectile gets to the center, otherwise the magnetic force will be pulling the projectile back to center after it gets to the other side, slowing it down. Since we have to deal with this pesky real world physics, there's a rise/fall time in current change that is dragged out due to resistance, so you ultimately have to switch off the coil before the projectile gets to center. There are a few ways to go about this, which is why engineering is so fun!

There's an entire EE degree to unpack here. The switch on time will be limited by the internal series resistance of the caps, best thing you can do is put them in parallel, which you've done, but when you do your calcs, don't forget to take this into account. For your switch off time, you want to use an IGBT - not a MOSFET. IGBT's are more or less the same but have better switching performance at high currents. I don't remember which ones specifically, but look at the IGBT's OneTesla uses in their Tesla coils. They sell replacements, look up that P/N and start from there. You may need to order a variant that can accommodate the currents your coil is drawing. Ballpark it by Vcap/(Rcoil + Rcaps).

Look up how to wire an IGBT as a switch and then use the gate as the on/off for your coil. Take a bottle of Adderall and watch very closely when the projectile gets to the middle of your coil and then quickly turn off the IGBT. Reaction time is key. When you realize you can't react that fast, think of a good way to use a sensor that will automatically switch off the IGBT when the projectile gets to a certain position. Perhaps an optical sensor, inductive feedback, or something. It will take some dialing in, but should get you there. There are a 1000 ways to optimize this, but this is a really great start and it's best to optimize one step at a time.

Keep it up! DIY projects and staying curious will get you much farther in your career than stereotypical "resume skills." When I interview people or look at resumes, this is one of the big things I look for - personal projects. To me, it means your curious, want to learn, and have a fundamental passion for engineering. Sure a coil gun may not be directly relevant to my company, but knowing that you understand the bigger picture - the product, the fabrication, iterating through failures, component costs - that is entirely relevant, and surprisingly a rare trait.

DM if you have some specific questions, I'll do my best to assist