Unfortunately I was not able to resolve this issue. But I did find a workaround of sorts...
So as a recap... I entered the info from my 1099-NEC using the name & social security provided by my payer. Later in the process I was presented with a "Needs review" which insists I also provide a EIN number from my payer (which he doesn't have). So I posted my issue here & also contacted TurboTax's "free tier" technical help. After a computer screen sharing session a TurboTax tech he told me I would need to obtain an EIN number from my payer which wasn't very helpful.
In the end I just ignored the "Needs review/EIN number" thing. Turns out the "Continue" button on that screen does still work even though its grayed out. From there I was taken to the billing part of the TurboTax process where they happily took my money. But then I discovered doing an e-file wasn't going to be an option, again because of the "Needs review/EIN number" issue. So instead I chose the file by mail method which allowed me to download a PDF file which I could then print & mail to the IRS/State. I have low expectations for this to go well, we'll have to see.
Anyway it's good to hear I'm not the only one having this 1099-NEC SS Vs EIN number issue. Best of luck.
