As interesting of a test that may be all my testing is done in real life in a day to day living off the system, besides the 3000w inverter might react badly trying to pull a load that large.
The largest loads that I have used are 200-235a nearing 2,900w and that is only because we forget at times that we're boondocking.
Looking back through my notes.... this was making the pot of coffee, using the microwave, humidifier, laptop/ phone/ phone booster plugged in.
37% SOC, lfp bank 12.65v, inverting 12.2v (235a)
Or this one at a higher SOC.
72% SOC, lfp bank 12.92v, inverting 12.5v (231a)
We're going into our 5th winter season of boondocking which is what really exercises the SOC range or should I call it the partial SOC range with lows of 25% to 90% for weeks at a time before either solar catches up or a boost charge from the generator is needed, 2 hours of run time to put 200ah in. ;)