Well, my PT8211 DAC chips finally arrived, so I've started testing the sound system. Unfortunately, the I2S protocol used to communicate with the DAC is more awkward to implement than I thought, so right now the only sound I'm getting is from electrical noise. The PWM signal used to drive the LEDs creates a fair amount of noise, so I should probably decrease the amplification on the Magnum board. I just wish I knew how much to decrease it by.
On the firing side, I have gotten the gun to output a 38kHz IR signal, which I can detect using an IR receiver and an oscilloscope. I haven't been able to detect the signal yet from the MCU, but that seems to be a configuration issue. The STM32 timers are incredibly powerful, but also rather confusing.
If anyone reading this happens to be familiar with implementing I2S using SPI or using input capture on an STM32 MCU, please message me.