True, this is what you're talking about: https://socratic.org/questions/how-do-resistors-affect-capacitors#:~:text=The%20larger%20the%20resistor%20%2C%20the,has%200%20Volts%20across%20it.

but they don't want to slow down the capacitor discharge, since that would decrease the force with which the projectile is propelled. They want to very slightly stagger the discharge of each capacitor, so that each capacitor discharges as the projectile is passing it down the barrel.

To do that, I would try using three solid state relays, and have each of them controlled by a microcontroller (e.g. an Arduino, or ESP32). Each relay would connect a different capacitor to ground (i.e. each relay would allow a single capacitor to discharge). That way the microcontroller could tell relay #1 to close, which would discharge capacitor #1, then tell relay #2 to close, which would discharge capacitor #2, etc.

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Edit:

Actually, sorry, I misunderstood. They're not trying to stagger the capacitor discharge. But it does seem like they're trying to accurately time the discharge of all 3 at the same time? If that's the case, a single relay + microcontroller would still be helpful. Maybe I'm still misunderstanding though.

Edit #2:

The reason I misunderstood is because many rail guns actually do use multiple staggered electromagnets along the barrel. If you do that, you would want multiple banks of capacitors to discharge at slightly delayed times as the projectile is passing their respective electromagnet.