Best Shade grass/ground cover

[PILOON]

The Ajuga is nice, and for a weed somewhat controllable. I also have Vinca (periwinkle)and that spreads slowly in the shade.
I have the same issue with downhill water. The Vinca and Ajuga seem to suffer when tread on though.

YES, ajuga has worked well for me, it is a creeper so you need to sort of spot plant it.
I also like white clover as a low maintenance ground cover in less shady areas.