Let's start over:
Alternator Rating: Typically taken at 6,000 rpm. The typical step-up ratio from the drive-shaft pulley to the alternator pulley is about 3:1. So, if y our engine is running at 2,000 rpm, steady state, you are getting the full alternator output. At 2,500 rpm, you are getting no more actual power from the alternator as this is limited by the size of the system.
Rating vs. Real World: About 90%, with diode losses.
Inverter Output: No better than 90% of input, to the maximum *STEADY STATE* rating of the inverter.
Charger Losses: About 15% of input up to the maximum output rating of the c harger.
Load: The total load on the alternator including all items. In the typical automotive application, this includes: Lights, computer, ignition, sensors , peripherals such as heater fans, AC, heated seats, information and entert ainment, and much more.
For round figures, use 4,700 watts (391 amps). Of which about half are mome ntary loads such as power windows and the like. About another 20% are tempo rary, such as heated seats, heated rear window and fog lights. So, for roun d figures, you are generally running at a sustained load of 150 amps +/-. L eaving about 30 - 35 amps available for 'the rest of your load'. And your ' additional developed load" is about 45 amps, or so.
Modern automotive electrical systems have vanishingly little resilience the se days. And why vehicles with a "trailer package" not only have heavy duty cooling systems, heavier brakes, heavier suspension and such, but also muc h heavier electrical systems.
You might solve your problems with a 400A alternator, should it fit.
It still would help to know the inverter rating. Really!
Peter Wieck Melrose Park, PA