My family would be more at a risk of leaving had I wasted money on a system that over produces 8 months of the year just to brag that my utility bill is near zero during a few hot months. IMNSHO
I was pulling your chain. . . Sorry, left out a smiley or two.
The '6K' mention was causing old man confusion, I was thinking about the EG4 inverter. You are likely going to want "more" this summer. The cheapest improvement is panels, based on your statement, I'd double it to 12K of PV, probably the simplest upgrade with ROI.
I still say I don't want to change my lifestyle. So, I'm comfortable using 50+KW a day before solar, so I spend money on solar to reduce my electric bill, then force myself into a bunch of energy saving behaviors to try and make it maximize my savings and improve the ROI. Ok, but I think we are skewing the ROI, since usage is not apples to apples. Opinions are like *ssholes

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You probably want to get past TOU for your savings. APS or SRP? Arizona has really low rates off-peak. Even on-peak with the latest bump, in July, SRP is only like $0.28, between 2-8PM, which is less than my Kid pays any time in MA. Then again she doesn't use 120KWH some days in July. I'm going to bet you have a 200A panel (At least 150A) feeding your house. A pair of Sol-Arks would take you to 100A (+ some surge) of output which covers quite a lot of demand. This is actually quite doable, without breaking the bank, and gives you a modicum of redundancy. With 100A of inverter output you should be able to pretty much run everything, no matter the demand load in an all-electric home. This would allow you to gradually move
everything to a sub-panel fed from an ATS arrangement. This means you don't have to do creative load balancing when demand exceeds 50A, which you must do if you don't.
You could just dedicate a few low use high demand items to the grid panel like the range, the clothes dryer and the hot water heater (HWH). Trying to float these loads manually or creatively with some ATS control is doable, this is in-fact something I currently have in place, which I want to eliminate. If my total usage exceeds 80A (
Don't forget the 80% rule, no more than 3 hours over 80% of rated load), I have ATS's that will cut my EV charging platform, and oven range directly to the grid. You might look into an EV load share switch, I'm using one one to feed my HWH and Dryer. These switches can be had for a couple hundred bucks, and have high/low priority output, in my case Dryer is high, HWH is low. Pretty simple inexpensive way to limit demand.
I think you will find your ~30KW of batteries will probably put you about where you want to be so you should be pretty close there for maximal ROI, and get you over the TOU humps most of the time, which is where you are going to maximize your savings. It will not take you through the night, and from time to time you may not make it thru TOU, but power is cheap off-peak here so, until the bragging rights bug hits you should be golden.
I have dramatically more panels, and will be expanding there, but I also have two(2) EV's so the additional panels really help to feed the EV's. The extra battery I have is multi-fold, for crappy winter production, to possibly make it thru the hottest summer nights, when there are production disruptions, and to allow me to bleed excess power from the batteries into the EV's in the afternoon after I get home from work. I was tapping into the grid quite a bit December thru February even with the extra battery (added Nov). To your $$$ point the extra $10K of batteries has a pretty long payback with $0.08/KWH power savings. I think there is an added intangible benefit with power backup, in the event of a grid failure. It can be a bit hard to put a price tag on that piece. For me I can't remember the last time my grid was down so meh

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You did it!, congratulations!, and I hope you are having some fun playing around with all this stuff! You've obviously spent more than a modicum of time evaluating options, be sure to post how you are doing in July!