Advice Needed On Recapping Power Amp

Timlub, Things that look simple not always are.  There is no such thing as "Linear Power Supply", unless Linear means "Unregulated".   In reality it is primitive unregulated switcher that operates at 120Hz and switches at max voltage.  Current from mains is delivered to capacitors in very narrow current spikes of very high amplitude. Amplitude of these current spikes depends on transformer, power cable, ESR of capacitor etc. while width of the spikes depends on the ripple amount that, in turn, depends on the load current (definition of the switcher).  In addition to current spikes charging capacitors you get also very narrow spikes at the peak of the (rectified sine wave) voltage when rectifier starts conducting for a moment in opposite direction to quickly snap back.  To widen this spike there are "soft" diodes (like HexFET), that conduct fast but snap back slow.  I'm trying to show that operation of such primitive supply is not as simple as it seems and the fact that larger cap works means only that safety margin for rectifiers still exists but was reduced and might be very small.  If we believe that designer put unnecessary margin by mistake that's OK, but I would ask him  :)

As for inductance - electrolytic caps are inductive.  Inductance of such cap is proportional to capacitance.  Increase in capacitance means increase in inductance.   Believe it or not, but power supply caps are in series with your speaker (circuit is closing thru them) and their inductance can affect response time.

@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".