The exact phase of the input is what I'm after. Using a LO would cause you to read the mixture of the LO and the input signal rather than just the input signal, and that means that you will never see the phase with the same precision as if you were to observe it directly because the two will have slightly different frequencies.

If you were to put both on a scope in XY mode you'd see the phase change directly over time.

But I like your two step approach, use the het to get close and then lock on to the phase.

So far I've not been successful without first bringing the signal up to the point where I can do it directly and then I don't need to add the complication of a PLL.

Injecting various levels of noise into the signal is a good test to see if the system would still work in less than ideal conditions and so far the answer is a hard 'no', it may well be that I'm past my level of competence on this but it's only been a couple of weeks so I will keep trying.

One possible approach is just to use a flash AD and move the whole thing into the digital domain. That has a bunch of other advantages as well, the signal is not particularly high frequency so that should be possible without breaking the bank.