I always had the Kelvin connection so that didn't need to be redone. What had to be redone was the load resistors. You can buy 300 watt load resistors for $30 or whatever. Turns out these have high VCR: voltage coefficient of resistance. In simple terms, as the waveform changes in amplitude, the resistor modulates its resistance, presenging varying and dynamic load to the amplifier. This becomes dominant, causing third harmonic distortion.
A great paper on this is from 1966 with the title:
Harmonic testing pinpoints passive component flaws. So the effect has been known for decades. The mechanism that causes it is complex though. Of note, it has nothing to do with heating of the load resistor as that happens over time. It has to do with micro-effect inside the load resistor at such high currents such as impurity of connections. Here is a starting quote:
Unfortunately, VCR is not a documented spec for load resistors even from high-end resistor suppliers. It is through experimentation the Dale power resistors have been found to have low-enough VCR. Alas, the 250 watt version is expensive at $180 each and you need four of them for 4 and 8 ohm stereo testing!
Worse yet, the parts are simply not available. See this for example:
https://www.mouser.com/ProductDetail/Vishay-Dale/NH250-400-1?qs=81LrLu1ylWBveqWvVGPieQ==
I lucked out finding an alternative from a UK brand, Ohmite/ARCOL:
https://www.mouser.com/ProductDetail/ohmite/nhs300-8r0-1/?qs=T7nPz1OZfaCYYWtzcKdZcQ==&countrycode=US¤cycode=USD
I was worried they would not perform the same but turned out they did. Benchmark was kind enough to send me their Dale dummy load and mine and theirs perform the same. The difference in cost is that the Dale resistors are much beefier with a larger heatsink. So they can dissipate power more easily. I chassis mounted mine anyway so that acts as a heatsink.
4 OHm Dale resistors are available but they are even more expensive at $213:
https://www.mouser.com/ProductDetail/Vishay-Dale/NH2504R000HJ01?qs=sGAEpiMZZMtbXrIkmrvidIpgiW9xqmWBjhwJWAFua5A=
Note that the VCR gets reduced by the damping factor of the amplifier. To the extent you have a high damping factor in the amplifier, you may get away with less. Or alternatively suffer from worse results with low-damping factor amplifiers.
As it turns out, I had used very high quality/precision Dale resistors in my headphone amplifier load. I thought at the time it was overkill as one does not need precision there but I spent the money on them anyway. That likely enabled me to measure headphone amplifiers with such low distortions.
The other contributing factor was the speaker connectors. Bare wire outperformed my non-name banana plugs. So I purchased locking, solid brass ones from parts express:
https://smile.amazon.com/gp/product/B00O3NTB28/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
The knobs on these a bit hard on hand but otherwise, they do a fantastic job of clinging to the speaker sockets. And are easily terminated with large hole for speaker wire and dual screws to hold it. It can accept wires as thick as 8 gauge.
I had used silicon wire with thousands of strands for my speaker wires. I need high flexibility in wires due to countless times I connect and disconnect the wires. John Siau from Benchmark suggested star quad cables. I swapped those for mine and found no difference. But there may be an issue with other wires.
The key here is that I had a platform to test all of these effects: Audio Precision Analyzer's ultra-low-distortion analog sine wave generator and Benchmark AHB2 amplifier with similarly low distortion. Without these, you wouldn't know if what you have is good enough or not.
The old setup by the way, would cap out at 105 dB SINAD and third-harmonic would not go lower than -110 dB. That is more than 20 dB shy of the final measurements. Here are sample measurements of AHB2 with my old load (ignore the low frequency components):
Compared to what it did with the final load:
Notice the difference in third-harmonic. Overall SINAD does not improve as much because it also has noise contribution.