Would WWVB work as well / better?
Actually, I had my wwvb ("atomic clock") receiver connected to my ntp server back on Red Hat 7 in the early 2000s. I had to tweak the driver of what turned out to be an identical receiver designed to be used with the British equivalent to wwvb (I think it was called MSF). If I recall, it was just 1 or 2 lines of code that needed changing. The code was a bit messy and could have used some cleanup. But, it worked. I don't remember the driver name. You'd have to pull the latest release to see if it was still in there.
Also, the wwvb clock I had was the only model that I could find at the time that had a serial output. I don't know if there is anything available these days with a digital output. You might be able to find a CMMR-6 module (maybe from an old atomic clock?) to roll your own. But, programming a commercially available SDR might be easier.
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update:
I just found a wwvb receiver module on e-bay. Model number WVB-0860N-03A. It might make an interesting project!