Say the MW pulls about 150 amps with PSW or 120 amps with MSW. Your new inverter is PSW ISTR, so use the higher amount.
Let's say your supper will be BBQ steaks on the RVQ, with garnish from stove top frying pan, plus "baked" spuds from the MW (two for 10 minutes), plus frozen veggies "California Style" (five minutes in MW), plus any salad and dessert. So that is 15 minutes of MW, but in 10 and then 5 minutes close together.
We do that no sweat with 450AH of AGMs. Also did it no sweat with about the same AH of Wets.
IMO you can do it easily with two of your Rolls. Don't need the third one for that.
No idea about the Li type batts. Can't see the advantage for your scenario at all. ( However, it seems from your posts you can afford to try it out, so that might change how you look at it! :) )