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