LB,
This is my personal idea of what you should do.
Install two inverters.
Why?
You have water pumps from the well and for the pool. They surge high currents and that could make the light flick a bit when they start.
Install the heavy loads in the 5KW inverter, Like the refrigirator, and pumps.
If the battery don't last on that unit then you have redundant power for the rest of the house.
Like DavidZ said, the refrigerator will not kill you if it has no power for a few hours.
My system is sized for 3 days with out power, using all electrical units.
Sounds like you are not living on a budget, and that's important for the following advice.
If you would of start over, I would Install 2 OutBack power inverters,
https://www.outbackpower.com model FX3524, they are pure sine wave inverters and the fans will not make any noise. The AC and refrigerator will like that type of power. You can stack 10 of them in parallel to get 35 Kilo Watts.
About the batteries, get 12 rolls battery, model 2 YS 31PS, order them from the states or Canada ( They are made in Canada ), they are a bit more expensive but they have 10 years warranty. They are 2 volts battery, 3400 amps, and if one fails you can change it and have less problems. ( 12 battery will form one chain of 24 volts ).
The investment could cost about $15K USA.