It sounds like you want more 120 VAC. Your Yeti is rated for 1500 W. Even 1500 W is a lot for extended battery operation - what are these "REAL appliances" you're talking about? There's a reason RV appliances which create heat use propane (furnace, stove, water heater). Same with 12 V (lights, water pump). Or both (refrigerator). Microwave and AirCon are AC only, and typically are expected to only be used when plugged into "shore power."
But even your 1500 W Yeti should handle a microwave for short periods (popcorn, not rump roast), as long as nothing else is running. Again, what are these appliances which need more than 1500 W AC, where you expect 700 W of panels to keep the batteries charged?
If you want more AC power when off-grid, you get a bigger inverter, connected to the batteries. 1500 W is going to draw over 125 A @ 12 V, so if you want more power for other than brief periods, you're going to need a big bank of batteries and hefty wiring.
Normally, if you then want AC when plugged in, you'd have a transfer switch to disconnect the inverter from the outlets, and connect them to the incoming AC line instead. The converter changes AC to DC, and requires you to plug into external AC power. When plugged in, it can both charge the batteries and power DC appliances.
I think you're saying you want to avoid that, and always have the inverter provide the AC power, but have a converter provide DC to the battery and inverter to support that. Not the usual method, and it would work in theory, but you'd need a MUCH larger converter than 90 A to power a larger inverter. It wouldn't even power a 1500 W one, which is what you have in the Yeti.