If I understand correctly, if you simply apply a greater voltage it doesn't necessarily allow faster charging and would just create more losses due to the voltage drop. I could be wrong, as I've never attempted this.
Continuing with more stuff about the pack...
The microcontroller that accompanies the CPLD ont he main BMS is a TMS which is probably an ARM processor by Texas Instruments, but I can't discern the rest of the writing to get a model number.
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It shouldn't be off by much at all, really. Most off-the-shelf single cell LiOn chargers apply the full charged voltage (4.2V) to the battery constantly, but if read while charging the voltage is within 100mV of the cell voltage, from experience. I've also seen this with 3-cells-in-series setups (11.1V batteries) with nearly the same result. So, extrapolating that out to 96 cells in series would be a difference of up to 9.6V. Probably incorrect thinking, but, I doubt there is a huge disparity in voltage readings during charging.
I'd have to say the supercharger pushing 404V (4.2083V per cell) makes some sense, since if the actual target voltage is 4.15V per cell (398.4V) then that's only 6V difference. I'd love to get some readings from an actual normally fully charged pack at rest though.