Indeed, my TinySA has some serious problems. I tried re-measuring today and the measurements weren't just nonlinear, they were off scale. Self-test failed: "Above Critical"
I've tried several SMA cables--same result. So it looks like it's toast. Maybe it was ESD but it failed over a few days, and ESD might be more sudden. Maybe it's just Chinese quality.
I pulled out my old regular TinySA (not the Ultra version) and it seems to function appropriately. Who knew?
All harmonic spurs on all bands seem to be below -43dB from the main signal, most at least -50 dB down, although the 15 meter plot looks borderline at -39 dB, but after this experience with these toy spectrum analyzers, which cost less than a tank of gas, I'm going to assume that if measured with a proper piece of test equipment the rig would be found perfectly compliant. At least at this point I should move on to another concern.?
Here's 20M: (looks great)

15M:

On 80 meters the 1st harmonic is down about -52dB. There's also some other garbage closer to the main signal but it's still below -43 dB:

Looks like I'm back in business!
Thanks for your help
73,
Jack, N6LN