grass. that's it.

Over the last several days I've been researching this. I saw several recommendations of thyme because of its shallow root system and another that suggested creeping phlox for the same reason. I'd really like something I don't have to mow because the slope makes it so difficult. Obviously I don't want to ruin my septic system though.

Thyme is lovely but needs to be weeded as it is not weed suppressing. If you can grow in your area Geraniums 'Biokovo'or 'Karmina' , they'd work for the sunny area and their close relative, G. maccrorrhizum (Big Root Geranium) would work for the shady area. Both types are extremely weed suppressing and will not harm your leach field. But you'll have to weed between the starts until they fill in. After that, they'll be no work at all.

Any kind of shallow rooted groundcover can work. Thyme, creeping phlox, mazus, blue star creeper, the hardy geraniums mentioned above. One of the best weed suppressing groundcovers I know is Rubus calycinoides, aka creeping raspberry or crinkle leaf creeper. A low, spreading plant (evergreen in my zone), this is great on slopes and very well behaved for a groundcover. I would encourage you to find something as evergreen as possible as anything that is herbaceous or dies back in winter leaves the soil exposed to winter rains and erosion.