The question was asked, and a suggestion was was offered.
In these times of the occupational health and safety Nazzies, I very much doubt it would be a highly popular solution though.
I monitor background radiation level here all the time (since Fukushima) have a geiger tube hooked up to a display in my kitchen.
The problem would be the very random nature of background radiation, its constantly changing, and not small changes either.
That is going to make it very difficult to detect and locate an actual low level source from any distance.
But if it could be modulated at a very specific frequency, something might actually be possible with time coherent sampling, a very directional sensor that scans, and the power of digital signal processing.
But the whole concept is extremely politically incorrect, and effectively dead in the water.