Let's address the capacitors:
You don't want big di/dt and inductance at the same time. That's because
V = L*di/dt.
Now, I ran some simulations. Check out the pictures. Notice the pictures that have very large di/dt. Also notice the pictures that DON'T have large di/dt.
The equivalent series resistance of a battery string is pretty big. Maybe 100 or 200mOhm. The equivalent series resistance of a bunch of capacitors in parallel is going to be around 1mOhm to 10mOhm.
Look at the parts that have the blue highlighted part. That's what the current is in that part of the circuit.
This is the current right at the mosfet drain.
This is the current right at the diode anode.
This is the current that the capacitor bank sees. Big change in current. It's taking one for the team. It's lower resistance is making it so the batteries don't see the big change in current.
Next will be the small di/dt parts...