@Tatus1969:
I forgot to include the 300A fuse (which is also for capacitors still a good idea) in the internal resistance parameters, it is estimated to have a DC resistance of 375 uOhm, as far as I can find information about that. But I don't see it back in your resistance estimates either or is it already included in one of the parameters?
@Kjelt:
I also simulated 4x BCAP3000s (which I own myself also), they need at least 2x 1 meter AWG8 to not pass the current limits and are then capable of supplying 100 Joule in 25 ms. So they are real "beasts", but a lot of power is "burned" in the cabling. If a higher voltage than 10.8V is required, this spot-welder would be unsuitable for more than 4x BCAP3000, at this moment, for the currents produced.
@SirJMD:
You are correct, the power supply should be the "CC first then CV" type of power supply, that is also what the circuit is simulating.
I didn't simulate a balancer, that would normally operate in parallel of the capacitors shown. But yes, I would at least recommend a "top balancer"/protection for these capacitors. It would need quite some "MOSFet switching" to be able to charge the capacitors individually, I think the current proposed solution with the CC/CV power supply with one additional MOSFet would be a more practical solution.