Why should a 50 % increase in RMS power result in +6 dB peak power? There's just no reason for that.
A "hefty power supply" (whatever the definition might be) doesn't do anything that cannot be measured. There are no miracles, anything else is audiophile dreaming.
Sorry man, it's PURE ENGINEERING (*) and simple electronics and EM.
It's the nature of the beast. RMS power requires a lot of sustained power.... Peak power is just that, short term peaks with little power, just a big swing in voltage but not sustained.
Power supply capacitors store energy, transformers handle the AC, rectifiers handle more power through them too. Increasing them is what we call a "heftier" power supply. Some power supplies are stiff (meaning they don't allow much over voltage ), others are loose ( remember the old NADs of yore that had a 6db swing from RMS to peak?). But those things are done primarily for increasing the long term, sustained RMS power of an amplifier.
For example, a "stiffer" power supply might increase the voltage from 48V to 64V.. that allows a higher output from the power devices. Remember that:
P = V^2 / R
Meaning that the power driven out is related to the voltage being output... and the output voltage is directly related to Vcc which is the output power of the power supply!
A bigger RMS rating in an amplifier, all other factors being equal, means more energy and larger swings of short term energy release. Remember that peaks do not have lots of energy in them... so doubling the steady power supply voltage will allow some pretty awesome increases in peak power ( that's what capacitors are for. BTW ). Also, low ESR caps can really swing quickly for those peaks!
Hence the gain in voltage peaks gain can be much more than the RMS gain.
Naturally, the output devices need to handle the peaks... but usually the upgrades of greater voltage parts and larger heat sinks ( for A and AB ) handle all of that.
Nothing audiophile here... just simple electronics.
(*) Have you ever soldered your way through an amp? Done schematics for it? I have.