Hi Aaron, thanks for the welcome and good to have your questions.
Vis a vis your grey water system: what's the norm there? Is this a hole in the ground with lots of rubble thrown in and the grey water pipes just discharging straight into it?
That would be what we call a soak pit here in Ireland. It's not recommended (nor legal) any more because it introduces the grey water down deep, close to the groundwater, and poses a fairly significant risk of leading to groundwater pollution.
Some more questions for you: how deep is the dry soil in your garden before you hit either solid bedrock that will stop water infiltration, broken bedrock that will let it straight down unfiltered, or water table. I've no idea what the Texan soil and subsoil conditions are like, but I imagine they are as variable as here.
Detergents: we just buy the ones in our
local health store. They are likely to be better than the mainstream commercial varieties.