Wiring Help

[amberpp1]

Thank you for pointing that out rmaddy, I've looked at that battery so many times now, I am not sure why I thought it ran on 24V. Silly mistake.
Right now I am planning on purchasing 4 more of the 12V 100AH SOK batteries to pair with the 4 I already have in a 4S2P configuration, I am also planning on purchasing the autotransformer as a solution to needing the two legs of 120VAC here in North America.
I do have a new question however, as I am trying to work with the man who just installed a deep water well on my property. Initially they thought the well would need to be 120 feet down and would require a 120V soft start pump. After actually drilling the well ended up being 500ft deep. The most simple solution they said would be to use a 240V soft start pump. I feel like this is a stupid question to ask, but if I am using the autotransformer will I still have the option to run a 240V pump off of the inverter? or will the autotransformer mean that's no longer possible?
Thank you all again for your input, this has been very helpful

 

[Hedges]

You can add a 120/240V autotransformer of some size to supply 120V loads from a 240V inverter. Use fuses/breakers to protect it from overload.
The 240V will still be available for pump.

Grundfos makes soft-start (inverter drive) pumps. But some people have said they die after a few years?
There are also 3-phase pumps (a bit hard to find) and VFD which run on single (or split) phase 240V and gently ramp up 3-phase motor.

There are also jack pumps, which work similar to oil derricks, with a positive-displacement piston pump down the well and motor above.
Typical deep well pumps can deliver far more water than your house uses in a day. They also draw down the aquifer more due to flow rate. You run them a small fraction of the time, and need high power for that short time.
A slower pump would run more hours at lower power.

Here's one brand. Don't know who would be best fit to small domestic application.

https://www.deanbennettsupply.com/pump-jacks.html