That's got to be one heck of an inverter! My 1500w continuous/3000w surge inverter has a 150A fuse on it and runs anything I need except the AC.
I've actually had great luck with modified sine inverters, but it depends on what you're trying to run with them.
I too like being able to camp generator free, but I'd rather run a generator than idle the pickup.
Are you planning to use the pickup and inverter as your main source of AC while camping?
The one in my RV now is rated for 3000W continuous, and 6000W surge.. it will start the A/C, but doesn't like to.. it typically beeps, shuts down... but comes back and the A/C is then running.. must be enough to get the compressor motor moving... but I try not to use it for the A/C.. it gets a 500A Fuse. I'd like to keep that inverter on during travel, and the Fridge on electric, to save propane, an minimize RV fridge fire risk.. mine had a recall where the put in additional sheet metal to contain a possible fire, but nothing to mitigate the risk of a leak and a flammable gas leaking out with an open flame.. That electric draw is about 330Watt, and that ends up needing about 30-40Amps DC from the batteries to run, and the trailer plug from the truck has too much voltage drop to keep up, it ALMOST does, but if the batteries on the RV still need a charge.. well not happening. I plan to add a heavy gauge winch type connector to solve this issue. I don't plan running the truck in place of a generator, the battery bank on the RV can handle it for a time, I'll be adding 90W solar to charge when off the grid, and I have a small 800W gas generator for charging when needed. Mostly the truck upgrade is to ensure I have plenty of power in travel mode.. and since it is possible to run A/C on my inverter.. open that up when it get really hot... with the dual alternators, it could run that. Also, I would like to add a Truck inverter, similar to what the RV has. It was fairly inexpensive, from amazon.com.. and that unit has proven to work well, a pure sine unit. The bad unit was a Modified Sine, 2500/5000 peak, Duracell (Xantrex) so should have been a quality unit, it never worked well from day one. It could barely run the microwave, and nearly caused a fire with a cordless drill battery charger overheat, that problem is apparently common with MSW inverters. Also the voltage drop with load was substantial, even the 300 watt fridge brought the AC voltage below 100Volts RMS.. The last straw that made replacement a must, it would periodically restart, under any load condition, and the Xantrex tech support had no ideas to correct issue... the pure sine doesn't go that low with 3000 watts on it, I've tested it. It is night and day difference. Also, it's some off brand China inverter that had good Amazon reviews.. ironically. I've also put in a smaller 12V power supply, and can turn off the original 950W converter, so I can use the small generator to supplement the batteries/charge and run any load when camping.. only a really high temperatures with A/C load would create a problem with this set up. It allows me to keep the 2400 watt, 75lb Generator at home and take the 20lb 800 watt unit, which is also very quiet and efficient.
Here is the inverter I used in the RV:
https://smile.amazon.com/gp/product/B0131PZ9J2/ref=oh_aui_search_detailpage?ie=UTF8&psc=1