The specified (typical) value for the phase noise (100 kHz, 1Hz BW) is -107dBc and for 1MHz -123dBc.
At 8MHz that phase noise is very high at those offsets! A decent spectrum analyser can measure that noise spec very easily.
However, you asked for a cheap and cheerful alternative and I would suggest the following:
Make a 'decent' 8MHz oscillator that gives about 5mW output and use this as the (ultra clean) local oscillator to a regular double balanced mixer. eg SBL-1 from Minicircuits or even a home made mixer.
You could use a decent commercial signal generator as an alternative for the clean LO but even with a modern lab grade $$$ sig gen the phase noise won't be anywhere as good as a decent homemade 8MHz oscillator at 100kHz and 1MHz offsets. But a decent sig gen should still be easily clean enough for your very 'noisy' requirements above.
Then feed your original oscillator under test into the RF port of the mixer after attenuating it down to be about -5dBm. Make sure the difference in frequency between the two oscillators is initially about 10kHz.
Then feed the IF port of the mixer into a PC soundcard via a 6dB attenuator and view the response on some freebie spectrum analyser software for a PC soundcard. You should be able to see the noise on the signal and this will be dominated by your noisy test signal at 8MHz.
Obviously, if your signals drift apart by more than the frequency span of your soundcard then you won't see the main signal appear on the PC spectrum analyser display. But you can then tune one of the oscillators away by 100kHz or 1MHz and just look at the noise at the relevant offset.