For a crazy idea on catching super-fast pulses look up the (very old) Tektronix 545 analogue sampling scope that fires a pulse "backwards" up a delay line against the input signal coming the other way, it's mad genius. It's a 30MHz scope that can display GHz signals.
You could use a similar idea to fire a chain of cheap ADC's from a delay line or somesuch.
Edit: Can't find detail on the 545 but here's a link to Jim Williams explaining why "old [Tek] scopes are better" and a few specs: Reading Jim Williams - 3.9GHz bandwidth & 10uV per division sounds pretty groovy to me.