Thinking about your problem some more, I think I might form some dedicated test gear for measuring the phase noise. Assuming you have standard test components lying around, I would split the vco power, amplify one signal and drive the LO of a fundamental waveguide mixer (with a dc coupled output). I would then take the other signal and send it thru some sort of time delay (like a resonator, quasioptic resonator, long length of waveguide, etc) and then send this second signal thru a manual phase shifter and then to the RF port of the mixer.
You then could adjust the manual phase shifter so that the mixer has a 0 DC volt output at the IF port. Now you have a delay line frequency discriminator. As the vco frequency dithers, the video output at the IF port of the mixer will dither in unison. You can read the amount of peak to peak frequency deviation readily by just looking at the output on an oscilloscope You can run the IF output into a low frequency spectrum analyzer (or ADC/DSP software), do a little math, and have the phase noise measurment. If the noise is very good, you might need a 30 dB gain low noise video op amp at the IF mixer output.
Rich