If the Project digs its big hole in the 1960s and 1970s the KGB will be hard pressed to find it or at least to determine its purpose and target it. They don't have a lot of intel and also will be hard pressed to sort through the simply HUGE number of AEC sites that dotted the landscape during that period. The DOE Legacy Management Office
https://energy.gov/lm/sites has a long list of AEC sites that existed during the period. For example the Mound site in Miamisburg, Ohio had a large underground building
http://www.mound.com/~gmgreg/pdfs/ne...l-building.pdf. There were also a number of shelters and other underground structures constructed by FEMA
https://en.wikipedia.org/wiki/Presid...gency_Facility. This only lists the PEF around DC, but doesn't state much about other facilities that must be scattered across the country.
http://www.coldwar-c4i.net/PEF/presi..._network_2.pdf
That doesn't even include all the other underground projects that existed during that time.
The issue for the Soviets would be how many warheads do they have versus how many targets would need to be serviced. If the site didn't look like a great target they might run out of warheads before they get that far down the list. The lack of activity around the site and the continuing lack of any other intel might just push the site down more and more.
Terry