Excellent test with predictable results.
You had a good sample (enough tries) and documented which is important.
30 years ago I did exactly the same... 2 similar amps (SS) with the only difference in and output caps and 1 of them heavily bypassed.
We played around for days and a few interested people attended.
Bigger sample size and thus the results were a tiny bit closer to 50%
You've probably read it, but the reason FR is there is for switch mode power supplies.
In a normal (50/60 Hz) power supply BIG caps are needed as the discharge takes place over about 14ms and the charging (to reach the full voltage again) is only about 2ms.
You can imagine the currents involved are short and peaky yet 2ms is about similar to a single pulse of a 500Hz sinewave.
So really slow.
The slowest rectifier diodes can manage several 100kHz .
It's only when these diodes are bypassed by caps (100nF or something) that they get slower AND start discharging the just charged cap aslo (together with the load).
Anyway in a switch mode power supply the swicthing frequencies (pulse that charges the secondary caps) is between 40kHz and 200kHz for the old and relatively slow power supplies. The standard designs that can be shop bought for litle money and made by the Chinese.
Note that these cheap power supplies are used everywhere and their lifespan usually is just a few years.
Simply replace all those caps after a few years (for better ones like FR) including the time bomb next to the heatsink and you are set for years again.
More modern and even smaller SMPS (can have smaller caps, inductors e.t.c. for the same power) used in LED lighting and other more hightech operate in the 200MHZ to 600MHz range.
circuits in satellites e.t.c. already work on 1GHz and are very small have a very high effieciency and long lifespan.
lets focus on the FR caps in cheap designs.
They must have a high temperature rating (the PS get hot as they are often sealed) and because of the (compared top mains fed linear PS) fast charge time of just a few micro seconds the caps need to be fully charged.
because of this small time it charges the currents are HIGH.
High currents and high ESR equates to high voltage loss over this ESR and high voltage + high current = high power loss.
High power means the temperature get's elevated.
These high currents and over time increasing ESR eventually breaks down the cap till it fails. (cheap PS story above).
To make the PS last a little longer newer caps are developped that have a very low ESR (and thus losses) which is important for THAT typycal application.
Bypassing won't help in this case as the majority of the current still flows through the big cap which is what we don't really want.
It's like having a 1 Ohm resistor in parallel to a 10 Ohm the 1 Ohm get's 90% of all the current.
When you look at the ESR and frequency you can see the 1000uF is not meant for SMPS but the smaller ones are.
a simple PS at 100kHz charges in a '400kHz' rate somewhat squarewave like pulses with high contents of harmonics and is why they emit RFI.
You can see the ESR is lowest between 100kHz and 2000kHz and suited for this application.
Now the audio part.
Discharging takes place continuously class-A current, idle currents and in case of high power amps in rectified audio signals.
They draw power from the caps that have been charged. If this is replenished in microseconds (SMPS) there will be no ripple as even the fastest full power (20kHz) discharge current takes several times more ms but in that time is already replenished many times.
Not so with linear because the charge time is several ms several 1000x longer.
The ESR for audio is not of importance (for bass that is) as the ESR is already tens of Ohms (and for HP'amps the discharge currents are only mA's) + the series resistance (output devise+emitter resistance+ output Resistance+ load resistance is also very high so it cannot 'do' anything if a cap with a low ESR is used (low at a higher freq and MUCH higher at audio frequencies) than a higher ESR (with higher value) cap at the same audio freq.
The problem is when you test the way you did above this becomes obvious.
Now where does tha housesound come from then and that bass tightens when a 100nF is put in parallel of a big cap.
The 'ESR' for 100Hz bass note is 16kOhm and is in parallel with a 2200uF cap (ESR = 4.5 Ohm) guess which cap can deliver in 100 Ohm ?
The small bypass caps are needed to ensure a low ESR at the point where fast circuits (digital or analog) draw very short peaks and to remain stable those large caps further away and the inductors formed by the PCB wiring create a high ESR at that point.
The 100nF lowers that LOCALLY so decoupling a power cap away from the circuit does in fact do nothing for local decoupling.
Where do all the differences in sound come from that are reported globally by thousands of people ?
Beats me... problem is in blind tests as done above it cannot be heard, only when one knows what has been done or seen what's inside and someone listens in that case the increase in SQ is there.
Always the same improvement.. stereo image, tightening of bass, separation of instruments e.t.c.
These things are deducted by the brain from signals that arive at the ear.
The brain is a funny thing..
Everything I ever researched (with my ears and test equipment) always came down to one thing.
Ears are great and music can bring pleasure... accurate instruments they are definitely not.
Neither are taste, touch, eyes and nose they are easily fooled and influenced by many many outside factors.
Now I know many will stand up and declare me a total fool for dismissing the many confirmed trials throughout the globe and it IS real otherwise there would not be such overwhelming evidence.
That part will remain a mystery for ever.
The few times both camps met and joined forces, the problem occured that the test conditions for either camp were not met, and when blind tests were taken the reported differences could not be shown at all.
Leaving irritated people behind with a wider gap of agreement.
So if you feel there is a big improvement doing what one does... it is there regardless of where it came from and I am all for it (contrary to my evil twin).
Changing bad bulging and worn out caps and increasing values will always result in improved SQ and is even quite measurable.
So I fully endorce Mike's upgrade kits... just for a different reason but the same result.
Improvement over SQ compared to what was in there.
It can even be measured I am quite convinced about that.
Who's right and who's righter that remains for the end user to decide and what their ears (brain) tells them.
One shouldn't care less about what other people with different ears hear.
) able to hear clear differences. But even then (as we already know from stated above 
Surely they are already in hifi heaven if they are at it. Yeah, they are still in the last century although not the middle when they died.
