Now why won't a 12V electric compressor work? And why does no one use it as the primary compressor in an auto?
Because in simplest terms it cannot produce the PSI necessary to convert the high pressure R134a gas to liquid at high ambient temps across a condenser(s)
See pic.
Blue is where the 12V compressor will "work". In red ...it will not "work"
For high ambients you must produce 300psi. A 12V compressor cannot do this without a Amp draw so high you will burn up your car.
Now in the red zone, your 12V compressor will run, but you will see 55-65F at the vents.
In the mid zone...maybe you will get 50F at the vents.
Only in the blue zone will your 12V compressor get "cold"
Take your pressures and post a pic. The pressures do not lie.
And maybe this blue zone and 225psi is all you need? Maybe so. Depends where you live.
But if you want cold air at high ambients, then run this system with a nice modern Sanden or equivalent and belt drive. Not a 12V compressor. Or look at one of my other post for how to run a 24V compressor and double your cooling capacity! It may still not be enough, but it will be better.
The modern rotary belt drive compressor on 911 AC retrofits has never been the critical path.
The critical path is in the other components. But it is not the compressor.