Advice Needed On Recapping Power Amp

@kijanki     Not to be argumentative, this is more for me to be informed. First, I've never added capacitance to a switching supply and This is just not how I understand inductance in relation to a power supply cap. 
Inductance would be creating a magnetic field, yet As the capacitor charges, the magnetic field does not remain static. This results in electromagnetic waves which radiate energy away. So the magnetic field dissipates. The cap itself is not inductive. 
So, I can see faulty, weak or under rated rectifiers.  Maybe if you flipped the switch at the exact instance when your ac was hitting its peak in the sine wave. 
Again,  I've done this a bunch.... The first time was in 1980.  Parasound built a chipped amp around a Sanken STK084... I called Dick Schram and he sent me 2 circuit boards, I ended up using an STK086, put higher grade parts in it.  His amp had 4 - 6800 mfd caps in it.  I used a separate supply case with 12 - 6800mfd caps.  That was my first foray into increasing capacitance and wow, what a difference that it made. 

and yes, I understand the 120hz "primitive unregulated switcher"  is not a switching supply. Sorry if I added confusion.

I think you'd need a particularly poorly designed power supply for bypassing to induce ringing. I'd say you're most likely to have that kind of issue if super fast rectifiers are employed. The rectifiers are what I'd worry most about frying. 

It is switching power supply, but unregulated. 

All capacitors are inductive (even piece of straight wire is inductive), some less some more. Electrolytic caps are in "much more" category.  ESI (Equivalent Series Inductance) can be calculated.

Capacitor becomes self-resonant at the frequency at which capacitive and inductive reactances are even - usually <100kHz (very low) for electrolytic caps.  At this Self Resonant Frequency reactances are exactly in opposite phases canceling each other and capacitor is pure ESR resistance.  Above resonance capacitor is more of an inductor then capacitor.

Amplitude of charging spikes is limited by ESR of capacitor, transformer losses and resistance in series (fuse, cable etc).  Lowering ESR of capacitor might increase amplitude of charging spikes beyond maximum current of the rectifier or max ripple current of capacitor.  These things have to calculated (and not just tried), otherwise it is "garage operation".

Well, I guess that I'm a garage operator.... I have always made sure that my rectifiers would handle the current, other than that, I've always increased capacitance without fear.  This is the 3rd time that I've worked on my Sumo, a couple of times ago, I replaced its rectifiers. This time I took it to a friends house and  I increased the power supply my self. He has the amp now finishing up a few mods and repairs from a lightening strike. I consider my old friend to be one of the best old school audio engineers ever. He is not as well known as some, but I've been with him rubbing shoulders with some of the best and trust him implicitly.