Hi Bruce.
I see no one replied so I will make some noise! Pun intended. What FUN.
Apparently some folks have considered placing the VNA into a spectrum analyzer (SA) mode. Hence, with some care you should be able to read noise power. If you precede the VNA with sufficient gain and a very low noise preamp, say below 1 dB, then the converted VNA as a SA could be used to measure the cold and hot state of a noise source. You can build a pretty decent noise source or find a used hp with an ENR of 15 dB. Then you can use the Y factor to find the NF of the DUT. This is a fun project.
GL, Regards, Alan