How are your skills as a necromancer?
Sadly lacking or else Cerebus wouldn't be going "Cerebus can see that 1ns peak is coming from junction capacitance there" (applies bypassing) "better, but why is the top of that square wave bowed, and why is it sloping down at the end if the input pulse is 100ns long, but not if it is shorter?" - Cerebus takes broadsword to LTSpice.
Seriously, I drafted, simulated and got this working (in spice) in an hour. Getting the linearity from ~1% to 0.1% was also easy, getting the 0.1% any lower is completely flummoxing me. I want to understand the causes and remedies before I start down the path of picking exotic hard to find low capacitance trannies. To be fair, I am trying to linearly stretch 50-100ns pulses to 1000 times longer or so (so they hang around long enough to count with a relatively slow clock), but in principle it is simple, but the devil is very much in the details.