The problem was in the plate i was using, which was kind of a thin but hard cardboard thing (back of a large mirror) that was really rather resonant and had a hard rim.
The signal, if you amplified it with a gain of about 1000, was clearly visible on the scope, but very difficult to actually filter in such a way as to extract the phase information. The reason its difficult is because you dont get one nice pulse, you get lets of pulses - reflections and resonances and so forth. You must extract the *first* pulse from both sensors to be consistent, which is hard to do, since its often super small.
Its not an impossible problem, just the material I was using made everything quite difficult.