Since lead-acid has a preferred charge rate, I would suggest looking at either Victron charge controller + Cerbo, or Midnight Classic + Whiz Bang Jr. These use a battery shunt to measure battery current and adjust SCC output to keep that at target CV/CC while delivering additional current for loads. Multiple SCC as required to deliver total current demand.
But if your loads are generally < 1000W as you report, just setting SCC for constant 112A (or whatever data sheet indicates) could be good enough, without using shunt to close the loop. A shunt and Ah or SoC reporting device could still be useful.
10kW of panels, half oriented SE and half SW, could maintain charging for a few hours in good sun. More to make up for seasonal tilt and light clouds/dust obscuring.
That's to maintain desired charge rate.
Now if your average draw is 500W, 12kWh/day, need to produce 1.5x that much.
Check an insolation calculator for your location. I'll assume 2 hours effective sun in the winter.
12kWh/day / 2 hours = 6kW of PV panels. About 8kW (STC) puts out 6kW.
So I'd say 10kW (STC) is a suitable array.
[Edit: I forgot to include 1.5x; make 18 kWh/day, 9kW output from 12kW (STC) of panels for 2 hours. So maybe a bit bigger than 10kW (STC).]
41 kWh of battery and 12 kWh/day gives you 3 days at 87% DoD (something you don't want to do very often!)
I'd say it is all well sized, if you put in sufficient PV and SCC.
Looks like 2x Midnight Classic 150 or 200 would do it (see curves for current vs. battery voltage)
[Edit: And by the way, I'd put some SE and some SW facing strings on each Classic.]
Probably other brands people here can also recommend.
[Edit: You can buy 12kW of panels new for $2400 to $3000, or a bit more depending on brand. Also various top names used presently similar price. It seems like used market doesn't acknowledge the glut of new panels presently being dumped for $0.20 to $0.30/W. Mounting hardware can add up, though - try to DIY with surplus/salvage material.]