Or replace it with a bigger one that has more output (and thus more drag on the engine), and upgrade the belt for longevity. Then the car's built in electronics will handle keeping the throttle in the right place for idle.
I'm in the process of designing a Sprinter mobile office roadtrip starlink vehicle with an asston of batteries in it, and upgrading the alternator so that the batteries are always charging from the diesel engine whenever underway is like step #1.
A high powered alternator and a carbureted engine with mechanical timing and nothing else on the engine but a starter, exhaust, flywheel, and cooling seems ideal.
That way you can set the starter idle for high RPMs to get the system up to speed with the resistance from the alternators and then set the idle speed at the ideal speed for the alternator to produce the most power.
But even on a 4 cylinder engine you're going to have horsepower to spare, so you may want multiple alternators wired in series with beefy transfer bars, so build a custom mounting plate for as many as it takes to almost bog down the engine at 1200 rpm or so.
These $350 alternators produce 220 amps at 14.6 volts at 1200 rpm, or 3200 watts each. I imagine you could run at least 3 of them on a properly set up 4 cylinder engine. That's getting close to 10 kilowatts of power before conversion and you would probably still not be taxing the system.
On the other hand, at this point you've spent $2,000 or so and a month of backyard engineering time to build an 8000 watt generator when you can buy a 13,500 watt generator at lowes for $1,300 dollars.
If you have a good motor you can run on a stand and a bunch of cheap or free alternators, then you just need the mounting system and inverter. Typical alternators put out about 40-80 amps, or 580-1200 watts. That at least has a chance of being cheaper.