Not sure where you are on the planning but I might point to some info and thoughts. I think you are correct that you have an inverter, not inverter charger. However that info is not all that well shown on online info! More "hints" to read past!
But some info if not found yet?
110wiring here:
What I see:
Looks like the inverter is wired on different 110AC breaker than converter input! Note 6 adds some info on that?
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View attachment 2510653
I think you will be correct in the converter is behind the load center. Do you hear a hum near that as is is normal for some AC hum!
I looked at the new parts catalog they give us but it is not working to get what I wanted for the ocnverter. I do see the 1000watt inverter in the compartment but no converter that I can get a look! I'm guessing by putting the note and info together that the converter is directly behind the load center and plugged in? That is not the norm as I find many actually part of the load center, but finding the true story is needed!
The biggie may be finding if the existing wire for in and out from the inverter as well as breakers are right sized for a new 2000 Watt? I think the converter portion is not involved for you!
Wish you luck as the planning can be the hard part!