You really need no more than 60kWh battery if your peak use is 40kWh only on worst days. This would account for 20% calendar aging and 20% reserve (10/90) for longevity. With your power needs <10kW you can still stay in 48V ( actually 51V with 16S LFP cells ) range.
So, you'd need no more than 1200AH at 51V, which can be done with either 200AH cells in 16S6P ( 96 cells ) or 300AH cells in 16S4P ( 64 cells ).
It is a massive battery and I would consider reducing the need for AC in some other ways if possible ( insulation, whole house fan, etc ) since AC is the killer app. However, this is doable if money is not a problem. I have seen such systems done a few times.
You will need enough solar panels to charge the battery, I'm guessing at least 10kW-15kW array, depending on your geo location.