Did some half-wit simulator wielding while Ampdog had a short(!) nap. Then we had a technical glitch with the forum. Kay, bless his heart, has fixed it by extending the confines of the playground for us. Now we have elbow room again.

Thank you most kindly Sir!
My "non-artists" impression of the transformer (300VA 2 x 35V) is done with coupled inductors and some series resistances added. 4 Ohm primary and 0.3 Ohm in each secondary. Then a bridge, and then 4700uF caps. Another of the same but with 47000uF caps. I start the whole lot off at (+ and -)38VDC, wait for 1 second (the caps still charge up further) and then run some 3 Amp(peak) triangles off the caps at 100Hz for a bit. Then the triwave source shuts off (after running for 0.5 sec) and we can see how things recover. I also added the 500mA drains (CCSs) Chip would have in his amp over the caps.
Basically, fig 1 is more or less what one might expect to see in terms of voltage ripple on the caps. Only the positive rail shown. Negative rail does the same but upside down. Red trace is voltage on the 4700uF and green on the 47000uF.
Fig 2 is the current flowing in the secondary during the same sim. Red in the transformer with small caps, green in the transformer with big caps.
The charging pulses become impressively low (with small caps) in an amp that has low (say 100mA total) quiescent current for instance, at least while there is little/no signal. Fig 3 shows the currents with only 100mA quiescent in stead of 500mA coming off the caps, same colour scheme. Looks nicer when there's no signal, but not useful for this particular amp that does a kind-of class A imitation?
Sooo:
With big caps, there's a somewhat more consistent charging current (pulsed) in the secondary winding, and a much more consistent voltage on the caps. Ie, things are more equaly horrible with lots of capacitance.
Now which to prefer? Big and sudden voltage swings or constant troubles in the secondary (and the primary)? Eenie meenie miny... I like stable voltage on the caps.
Why?
'Cause the amp as it stands has limited power supply rejection. And I like to think the amp isn't as hard-wired to the transformer as it is to the caps.
On the other hand, the smaller caps might sound more funky. Due to the voltage step on the rail making it's way into the amp, at the beginning, and after a nice big musical wallop. So the wallop starts with an extra "plop" and the next mains cycle after the wallop then becomes a sort of point at the end of a sentence, as the voltage step from the recovering rail feeds into the amplifier circuit. (OK I exaggerate a bit but I'm not enthusiastic about that sort of thing.)
@Ampdog
How would one measure this Ampdog? With a single pulse longer than a mains cycle and looking at the settling behaviour on the amp output? Wish I had a 16 bit scope *with* bandwidth.
@Everybody clever
Any of the actually clever guys reading this ever made a proper model of a T'Tech 300VA toroid with a core that saturates and everything that opens and shuts? It's sort of what I half-tried but I could well be way far off. My voltages look a bit low for 2 x 35V secondaries. Care to share before I make more of a fool of myself? What should the coupling factor between the inductors be for a mains toroid in SPICE? 0.995 like I did here? 1 looks too good to be true.
@Handsome
Do you have a model number for that MF amp? Sounds like power factor correction (which is a fine form of good-neighbourliness. We shouldn't complain about the quality of the mains when we've been polluting it.) So it could be good, but I wonder about the regulation and stuff. Would like to see it.