100 kW transmitters on SW is just kind of middle-of-the-road
500 kW, and more, is not all that uncommon.
As you have found out the frequency readout and resolution of general low end tube type SW radios like the S-120 is not great. In the case of your station if you could have told the real frequency you would have probably been able to ID the station. 7 MHz to 6875 kHz is a pretty large error, but not uncommon with this kind of radio. The scales are too course, the indicators too wide, and the calibration not so great.
However, there are a couple of ways to resolve this issue and to know what freq you are really tuned to.
One would be to add a digital readout that tracks the LO, these are not expensive and work OK. But, they are also not “old school” and in my opinion if you are going to do that you might as well have a newer radio with digital readout.
Another way, and the most common way we did it “back in the day” (damn, that makes me sound old) is a crystal calibrator. A crystal oscillator put out tones at known frequencies, say every 100 kHz, and by tuning to those tones you could tell “about” how far off your dial was, and get pretty close to the right freq. For BC stations this was often close enough to make an ID.
The best way, in my opinion, and still old school, is to use something like an SCR-211 / BC-221 or LM series heterodyne frequency meter. These are consistent with what might be found in a better heeled listeners shack in the 40’s to 70’s, and can yield frequency accuracies of well under 1 kHz, with no modifications to the radio. One freq meter can service multiple receivers, so you really only need one per shack.
My introduction to the BC211 page here, also explains how to use it with a boat anchor and why you sometimes have to use them with such radios:
My BC-221 and LM series Page
Manual for the SCR-211 series here:
http://www.w7ekb.com/glowbugs/Military/PDF files/BC221/SCR-211.pdf
T!