Self's "5532 Low Noise Unity Gain Balanced Input Stage"

Looks like measurement grade 😀 onboard audio, or something not very far from it... the 0.05-ish dB periodic ripple is telling. Good enough, anyway.

I think the idea would be comparing a straight loopback vs. a detour over -80 dB --> LNA. (The ground loop may need to be taken care of.) At least I'd expect much better accuracy from that when compared to using the signal generator as a source. You should have 20 dB of difference, pretty much all the rest is your gain error.
 
Looking through this thread, I noticed this:

The lowest result was -84.41dBV @ 8kHz while the highest was -80.76 @ 400Hz. The average was -82.00 dBV.

I just remember Douglas Self's capacitor distortion test, and some of the (film) caps peaked at 400Hz. So, I think a mild improvement might be accomplished by using different capacitors. Any opinions on this?