Hey Jack!
I suppose one of the main points on the charge rate would be the battery capacity/chemistry type of the batteries. For example, the internal resistance of standard ni-mh batteries usually limits them (safely) at 3C, 3 times the capacity of the battery. For example, 1.2v at 800mAh would have a maximum output current of 2.4A with a voltage dropping proportionally.
I think that if you try to charge the capacitors at a current of 1A to 1 time constant (63.2% charge) at 1A it would take about 6.4 minutes (T=RC, T(ms) = R(ohms)C(uF) 1A at 400V is a resistance of 400R, 400R x 970uF = 388000ms OR ~6 minutes)
Unless you don't mind the quite long wait (if I worked that out correctly! XD) I think you will be in for designing quite a high current switching circuit. Even at 4A, the charge time will be 1.6 minutes for every time constant.