The US holidays and other matters have kept me out of the lab for the last few weeks, but I think I now am able to focus a bit more time on the project.
At Theremino's suggestion I looked in depth at their circuits and did a few simulations with their LTSpice models. I am deeply thankful for their open source attitude and hope my stuff will be helpful to others.
For a simple gamma counter it appears that a standard Schmitt trigger approach will give the pulse detection and duration data that would be needed for that. The peak detector required for realistic energy calculations is a bit more troublesome for me. It looks like the video industry has pushed technology and costs down to a point where a high speed peak detector is feasible. If the pulses were captured/recorded in an analog form it would be possible to do this in post processing. However, to digitize it things get more complicated. A standard 44KHz audio capture would likely be too slow to prevent aliasing. The random, non-repeating nature of the pulses prevents a "stacking" approach.
One way I have looked at, which seems overly complicated to me, would be to have a very high speed A/D converter that is triggered by the Schmitt trigger in a one-shot manner. Since the pulses are very short (nanoseconds) the A/D converter would need to be able to capture at several hundred Megahertz. Both TI and Maxim make a 250MHz sampling unit that would work for about $25. For a 200 nS pulse that would allow about 50 samples to be acquired from the pulse.
But most of the lab devices I have read about are using some form of Pulse Height Detector (PHD) rather than sampling the entire pulse. I have tried a few designs for a PHD but my simulations are not working reliably.