I found some documentation/app note from Matt here https://quantasylum.com/blogs/news/speaker-impedance-measurements
He measures a 4 Ohm speaker impedance and the data looks great. There are some suggestions for using FFT Size that might improve things: using a chirp that lasts 1 second.
Key Point: Use a 64K or higher FFT at 48Ksps. This will yield a chirp that is just over 1 second, and it’s accuracy at resonance will be within a few % of the value seen with a 128K or 256K FFT.
However there is a note about using the QA460.
Key Point: The QA460 is designed precisely to help you make speaker measurements, but you might want to increase the shunt resistor to 0.1 ohms or even 1 ohm, depending on the accuracy you need to see in the resonant peak amplitude. It’s not uncommon to see resonant peaks of 20 or 40 ohms when measuring speakers. The good news is the sense resistor doesn’t have an impact on resonant frequency–just the accuracy at peak resonance.
If you don’t fancy swapping out the 0.01 Ohm current sense for a 0.1 Ohm you could use the impedance test fixture PCB I made. This way you can use the QA460 to drive the load but use whatever current sense resistor you want. There is a thread for that and Gerbers + BOM on GitHub Comments welcomed on test fixture PCB for impedance measurements - #11 by Dan
Finally, I’ve been making a reactive load for my guitar amplifier, and get similar data to you when I take measurements. As the impedance rises the voltage drop across the current sense gets smaller and noise appears. It seems like I too could improve these measurements!
Solid lines are my simulations, others are QA403 + QA460.