I think you may be misinterpreting regulations. There's grid-powered and grid-tied. Grid powered just means you're using the grid to act as backup power for your "off-grid" system. There is no restriction from doing this. Grid-tie - where you can actually back feed power TO the grid requires permission and permitting depending on the authorities in your area (city, county, power company, etc.).
Also living in your state, I can promise you there are no state regulations that prohibit grid-tie systems or connecting an inverter to grid solely for the purposes of pulling power from the grid.
Saying you can't power an inverter with grid power is like saying, "you can't charge your golf cart from the grid." It's just a device that uses grid power.
Okay, so 12.4kWh/day assuming 18 hr/day run. That's probably very high if the insulation is good, and assumes the unit runs at max power for the full 18 hours - probably not the case.
If you're on a phone, turn it sideways, and you'll see my signature below each post I make.
Here's the results from link #5 for Tucson:
Using 5.55h for Sep (meaning you'll produce more Mar-Aug), 12.4kWh / 5.55h = 2.2kWh of panels. Round that up to 2500 to be sure.
You need 12.4kWh of batteries.
I'm not familiar with BYD cells, but if you built your own using the Xuba 3.2V 280Ah cells, you would need:
12400Wh/3.2V/280Ah = 13.8 cells. You'd need to round up to 16 since you need multiples of 4 or 8.
That would run you around $2000 total including the BMS.
You'd need 10 battleborns ($9500).
You could get 2500W of panels from Santan Solar for $700 right now ($70/250W panel).
One of these:
https://watts247.com/product/pip-lv2424-msd/ - another $700
This is likely a worst case. This might be way less. It's impossible to know for sure unless you actually have the daily energy usage of the units in question.