GHz class sampling oscilloscopes on the cheap
Repetitive waveform samplers work well (for repetitive waveforms!)

The comparators specify about 10pS delay variation with input overdrive voltage varying between 50mV and 1v, so if you can tolerate that dispersion on your timings (and it's comparable with the TMU resolution) then you've got a go-er.

I'm building a 32 bit DAC at the moment. Not because I need a 32 bit DAC, but because I want to find out what the real hardware limitations are that will prevent me achieving the theoretical numerical performance. I suggest you build your digitiser in the same frame of mind!