This is looking more and more interesting.
The Apollo Operations Handbook for the Extravehicular Mobility Unit, Volume I (system description) for Apollo 14 (which covers the early pre-J missions) says that each PLSS generated two subcarriers, one for PLSS telemetry and the other for an electrocardiogram. EVC-1 (worn by the commander) put the EKG on a 5.4 kHz subcarrier and telemetry on 10.5 kHz. EVC-2 (worn by the LMP) put the EKG on 3.9 kHz and telemetry on 7.35 kHz.
The LMP's PLSS transmitted the two subcarriers, plus the LMP's voice, via VHF-FM to the CDR's PLSS, which mixed in the CDR's voice and his two subcarriers, transmitting the whole thing (combined voice + 4 subcarriers) to the LM by VHF-AM.
The block diagrams show the subcarrier oscillators as VCOs (Voltage Controlled Oscillators), which means the telemetry frequency modulated these subcarriers. The modulating signal commutated among 30 analog channels 1.5 times per second. 26 channels were used for actual telemetry and the rest for synchronization and calibration. Your mystery signal sounds exactly like a frequency modulated tone (though lower than any of the frequencies listed above) and repeats 1.5 times per second (rather than 1.0 times/sec as you'd expect for most time codes).
So my very VERY initial take is that you've found one of the two PLSS telemetry streams, shifted down in frequency to make it easier to record on one channel of an audio tape recorder. It's probably not one of the EKGs, which was transmitted on its own subcarrier, and in any event would not repeat at such a fixed rate given the astronauts' physical exertion (not to mention excitement).
Got any more like these?