Okay, so the trusty old Singer CSM-1 isn't so trusty, but I did find a workaround that allows it to work perfectly. Almost.
It's 10 Hz off, but hey, you would be too after 40 years of service.
I did the first of the measurements last night and was absolutely blown away by the raw sensitivity of the amazing little SDR. Starting at 100 KHz with the upconverter active (so we're looking at it's sensitivity as well), the sensitivity was -62dB. Not a very good start, but we're at a pretty low frequency. Most wide coverage receivers are crap down there anyway. I started testing every 100 KHz, and the sensitivity went up quickly. By the time I got to 1 MHz, it was up to -100dB (up to?). From 3 MHz and up, the sensitivity was at the maximum I could measure with the CSM-1, -110dB. That's as sensitive as my Yaesu FT-857D, which cost an awful lot more than that $20 SDR module!
At 70 MHz the sensitivity started to drop off, until I realized that I was reaching the limits of the Ham-It-Up upconverter. I switched it out of the circuit and continued on all the way to 550 MHz, the upper limit of my CSM-1 (the SDR measured -110dB at all frequencies). Technically it can go higher using harmonics, but the output amplitude of those harmonics won't be at the calibrated level. Good for frequency testing, but not for precisely measuring sensitivity.
So, in it's current configuration, this cheap-as-beard-dirt SDR module is very, very sensitive. However, it's still wide open and noisy as anything.
More testing later, when I start playing around with various filtering circuits and ideas.