Everything looked fine (albeit enormous) up to the 52,000Wh per day line.
If you're planning to go that big (and that's quite big, by any standards) you're better off with a 48V system, or 24V at the very least. Anyway, for the sake of argument we'll assume you stay with 12V.
52000Wh / 12V = 4300Ah required per day. Let's round that up to 4500Ah, to acount for system inefficiencies.
If we assume that your average 125W panel will put out 10A at 12V, then that panel will need to stay in full sun for 4500Ah / 10A = 450 hours, which assuming that you do get 8 full-sun hours a day (5 or 6 would be more common) would come to 56 days.
So if you want to recharge your batteries fully each day and use 52kWh of electricity, you'll need about 56 of these panels.
Now for the battery. The usual procedure is to have enough capacity that 3 days of no input only drops the battery to about 70% (ie. you've only used the top 30% of its capacity). To do that, you'd need 4500Ah * 3 days / 0.3 = 45,000Ah of capacity.
That will require 147 of those batteries you mention (so it's a good thing they're AGM and not flooded cells that you have to top up every month!)
Alternatively you could purchase a suitably sized generator for cloudy days, and that way you'll only need about 1/3 of the battery bank, or about 50 batteries.
Of course, if you eliminate the air conditioners from the equation you only need 12kWh (1000Ah) per day, which would let you get away with 25 panels and 32 batteries, or 11 batteries if you use the generator for cloudy days.
This is why relatively few people try to run air conditioners from solar PV systems.
BTH
(24V system, 560W of PV, 1000Ah of battery, harvesting approximately 100Ah per day).
