High current linear PSU capacitor requirements
Electrolytic caps have rated max ripple current (usually about 2A or
  so, even the "low ESR" ones).


I don't think so. Take a look at these: -



On standard AC supplies using a bridge rectifier, the ripple current can be higher than what is implied by the load current. Consider that the cap discharges (due to load) over nearly half a cycle then the energy is returned back to the cap as the incoming voltage peaks near maximum. The time period of the re-charge can be as low as a couple of milliseconds and it may have to push 10 x load current into the caps for this limited period. This is also why you'll probably have to rate your bridge diodes as 1000A peak.

But please do a simulation to see what happens. This is important as your power supply requirement is more than 1kW.