Hi Frank, sorry, I had some easterly distraction and also I had to think a bit more about your problem.
You have to convince me, that you have a problem with high noise in the preamp. I do not see that yet, but I am open for your arguments.
* you could disconnect the preamp from the QSD
* put 50 Ohms to ground at the input of the QSD
* measure the noise (in dBm)
* that is your noise baseline for the QSD (mixer, Si5351, opamp)
* now disconnect the 50 Ohms and connect a signal with constant level to the input of the QSD
* measure the signal level
* calculate SNR for the QSD
* now connect the preamp again
* put 50 Ohms to GND at the antenna input of the preamp
* measure the noise level [in dBm]
* disconnect the 50 Ohms resistor
* put the same signal source to the antenna input
* measure the signal level
* calculate SNR for the whole system [preamp plus QSD incl. mixer, opamp]
Maybe there is some easier way, but at the moment the setup above should show, whether you have a problem with noise in the preamp or not. I think your 30dB difference is mainly an artifact of the grounding of the FET output, which has some side effect on the whole circuit, because you did not isolate / disconnect the preamp from the QSD.
If you have a spectrum analyser and a calibrated signal generator, it is much easier to measure the noise figure of the preamp alone (again, do not GND the output of the preamp, but disconnect it from the QSD before any measurement)
I am not totally sure, but as the input/ouput of the preamp and the input of the QSD are designed for 50 Ohms impedance, it is probably wise to use 50 Ohms and not short-circuit any input/output for measurements.