Using battery power to go off the City's power grid

The analogy is correct and your statement regarding all the connections are also correct.  Power conditioners like the Shunyata and the Puritan can and in my experience do benefit from an inverter/battery that sits upstream.  It could be because of the cleaner AC or electrical isolation but I'm not 100% sure.  So that's why I demo and listen.  I don't like to just wonder if something is good or not. Part of the fun for me in this hobby is to try and experience various audio gears. It's all about the experience for me.  

The Amperetime battery and charger and the Giandel inverter arrived over the weekend.  Now I'm just waiting for the battery cables to arrive and then I can hook up everything and demo.  The AC adapter I made previously for the 30A RV connection has been modified and will now connect to the AC terminal block of the Giandel. Like oeno, I don't simply connect the Shunyata/Puritan to the 15A or 20A outlet.  We utilize the 30A+ outlets. 

One correction I want to make. I no longer have the Shunyata Everest/Omega XC combo. I now have the Puritan PSM1512 conditioner with Ultimate power cable.

My near term goal is to get back to the performance level when I had the Ecoflow and Shunyata combo. I'm not there yet with the Bluetti and Puritan combo but I'm hoping the Giandel and Puritan combo can get me there or even top it. 

Terrific!  I had thought the Giandel just has standard 15A outlets.  I doubt that a 30A outlet would be better for sound quality, although it will enable higher power demands.  Adapters can degrade the sound, so plugging the Puritan with the Ultimate power cable directly into the 15A outlet of the Giandel should be the purest way.  I would be incorrect if the Ultimate cable already has a 30A male connector.

My Shunyata 6000 is plugged into the 15A wall outlet, will much more clarity and HF extension than no Shunyata.  I am not interested in high power.  Most of my music only requires low power, with occasional peaks.  Clarity and resolution are appreciated mainly at low power.  That's why high quality class AB amps offer  class A operation at low power, and then AB when high power is required.  The ear is most discriminating at low power.

In any case, you can try the 15A and the 30A outlets on the Giandel, and see if there is a difference.

When I play music with my active speakers, the total power draw for the system is about 220W.  And when I listen to the headphone system, the power draw is even lower. So 5000W from the Giandel is overkill from a pure power perspective but I think audio quality comes from the parts and wires that can support that 5000W power draw.  For example, on the Ecoflow, I studied the parts and wires for the 30A outlet vs the 20A outlets and they are different.  This difference should cause a differece in sound. Being the tweaker that I am, of course I will test this theory on the Giandel :) My experience with Shunyata gear over the years tells me that wire gauge and quality matter and the quality of the parts and connections matter.

I agree, the AC adapter I plan to use with Giandel will have a negative effect but I have a hunch this will be overcome with the "higher quality" connection on the Giandel.  We will see.

I looked again at the Giandel site, and I see four standard 15A outlets, plus a hard wire connection for high power appliances, to the right of the four outlets.  I don't know if you are planning to use this special connection, but it would be interesting if you do, to compare the sound of that to one of the 15A outlets.  With your low total power draw at 220W max, any of the 15A outlets should be enough.

Also, they said that the Giandel is overbuilt with special EMF filtering.  BINGO, that alone may explain the sonic superiority of the Giandel as heard by Oeno.  I await your exciting experiments.

My concern is that Giandel advises to turn it off when not in use.  I don't know why.  This would be a problem with amps that need continuous low power for standby.  The manual cautions that if the battery voltage drops below 9.5, the inverter will shut down. That doesn't leave much room for the draining battery starting at 12.6V, so you would have to keep the battery charger running all the time, disconnecting the charger for critical listening.  Ricevs says the sound is not as high quality unless you disconnect the battery charging cables.  See what you find if you keep the charging cables connected all the time, which would be convenient.

I do plan to use the special connection on the Giandel. The 4/0 gauge 1 foot long battery cables arrived this morning and I’ve spent a good chunk of my evening connecting up everything and insulating all bare electrified metal. A word of advice, the Giandel has internal capacitors so to avoid sparks from the initial connection with the battery, it’s recommended to use a resistor to charge up the capacitors.

The battery is charging up right now and I’m waiting until full charge before I have the initial listen which may be in the morning.

I did not know about the EMF filtering which is good to know. The casing of the Giandel is all metal which I think should help with EMF as well.

I plan to charge the battery during off hours and then disconnect the charger during other times. And I want to do this automatically using relays and some type of smart controller.