Thanks. Very likely is RR, as my dial could have been off a bit. In fact, as I just heard the two CW "Rs", it is Radio Reloj.
I'm in Pensacola temporarily, right near the Gulf of Mexico, so a direct shot across the water. About 500 miles, plus or minus.
The old radio is a "super-sensitive" Sony TC-7, purchased in 1975 in Fiji. A radio that was well made at the time.