Advice Needed On Recapping Power Amp

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.   

Well I always liked extra power until I realized that in Toyota cars and trucks everywhere everything is perfect at any time and can’t be improved without trade offs — that what was just pronounced by my 2002 Tundra 5mt v6 466 kmi all original afrer 23’ camper long haul 1200mi from ski resort.

It was lovely white winter this year!
Would never mind the other one

Polar Bear
(I.e czarivey)

Well, I guess that I'm a garage operator.... I have always made sure that my rectifiers would handle the current

I've been in garage operation when I was 16, building EL34 100W amplifiers with components I could find around including chassis made of heavy aluminum trays that fish store nearby tossed out, but when it became my profession for the last 40 years I've learned not to do anything that I don't fully understand.  I would like to understand how do you know what peak current thru rectifier is.  Did you calculate it and how, measured it or just used rectifier that seems to be working? Did you consider max ambient temperature or max line voltage?  Did you consider shorted output condition?