You must be on the side that the all amps sound the same unless it isn't clipping.
I'm even more cautious in such opinions.
I'd say all the amps sound the same if they work with all possible and measurable distortions in "non-audible" range.
Clipping is not the only one reason to get some distortion.
For example, Matti Otala, founder of Electrocompaniet, "discovered" some TIM distortion and eliminated it his products.
Some russian company also claimed they have eliminated some weird kind of distortion (their know-how) and they are making some studio amps (CSA, CSB and CSM models). Our local sound engineers found their amps as great bang for buck at least.
On other side there are lot of amplifiers without feedback and they are also successfully being sold for crazy money, and even some sophisticated amps like CH Precision M1 with regulated amount ot global negative feedback which changes their sound and distortion profile...
We can go on for long time, but my main concern is that we never listen for sine tones (or even static multitones) into resistor and all these measurements can help us to distinguish crooked crap from well-engineered amp but they are barely usable when we try to find better one well-engineered amp of two.
There are lot of situations where difference must be not audible, but it's obvious and force people to buy one or another expensive unit.
really would like to know what science says about my question
As an some kind of engineer, I'd say that only properly done experiment will prove a lot of statements in sufficiently complicated system.
So I'd recommend you to try multi-amping (because in your case only impedance dips may cause some troubles) or get some power amp with moneyback option.
Some other solutions in 2-3 K$ range may exist if you are not satisfied with your setup. Like exchange of your mains to some big bookshelves of better class because you don't need anything below 80 anyway.
If you want my opinion about apm measurements, I'd say we can't really predict amp performance beyound basic requirements unless we know what was a technical requirement for design team.
Maybe they managed 0,002% of HD at 1 Khz into 8 Ohm resistor and didn't even try to use this amp at any real-world speaker (which is very realistic scenario for small hi-fi systems with bookshelf speakers included). I've tried few small cd receivers in big shop on some B&W 70x small floorstanders. It was total disaster even at reasonable SPL, I'd say.
For correct measurement I'd prefer to connect some voltage/current real-time registrator (like fluke norma) on real speakers and compare output waveforms with input ones.
Then we'll see
real amp distortion numbers in
real scenario, and I'm not sure that they will be much lower than those of good modern speakers.
But it's really expensive and troublesome to do and you'll have incredibly bad numbers for some audio review magazine, so I assume only some of best amp designers do something alike in-house during RD process and never show any results.