From 100 to 200? This makes things significantly simpler. (I don't know, how yet, but certainly it does) It's a variation by 2x order and not 800.000x. We get whole 100us to start the system, apply corrections to the start moment count, discharge capacitors etc etc plus 200us of "leisure time" between pulses. Sounds like you could get to do it with a standard or slightly increased speed micro, like ADuC824/834/845/847.

Does anyone here have experience with 24bit ADCs? How precise -really- are they? If they are really precise, this way you could do it with one capacitore (or a few in paralell, to repeat measurements and average them for better precision, or to redirect different pulses to different capacitors.) You'd still have 4 bits left to contain all nonlinearities, noise etc.

>------+--------+-+-+-+-+
in     |        | | | | |    _
       |        +---------->| | analog switch
     INT       | | | | |   | | 
                | +-------->| |
                | | | | |   | |
                | | +------>| |
                | | | | |   | |->-- ADC
                | | | +---->|_|
                | | | | |
           C1-5 = = = = = 
                | | | | |
                +-+-+-+-+-V GND

(plus 3state buffers to enable discharging)

Falling edge signal starts the procedure, ADC measures capacitor values in sequence comparing them against a lookup table (you HAVE to calibrate the device, the calculations required to create the tables would be probably too hard - differences in capacitor leaks, line lengths etc), this for say, 100us then the capacitors are all set to discharging while MCU performs some scientific averaging (discard extremes etc) on the values. Use ADC to find a preset "zero value" on the discharged capacitors about 80us later, lock and wait for new pulse (or use the granted free 120us before next interrupt from then to perform some communication with the outside world and make some use of the computed values).
The limiting factor is the ADC speed and/or precision (repeat readouts to increase precision, using more time) - If you use ADuC845/847 you get 1200 cycles of MCU for one 100us phase of the operation (readout, discharging, charging 1st half (100us free), charging 2nd half (waiting for interrupt)

Also the question is how much will a capacitor lose due to leaks over the uncertainity period of 0.12us of one cycle variation when the measurement starts.