Ground covers are naturally invasive, that is why they are considered ground covers.
My variegated vinca handles direct sun all of the time. I don't have any real shade on my property. The vinca on the upper slope has never been truly cared for for nine years and has not been invasive because there is little soil there and it can find some purchase between some of the rocks. It stays put.
The vinca behind the rose is covering an almost vertical rock wall and the only place it has truly become invasive is when it topped the wall and started growing under the dogwood tree. The shade provided by the tree, is giving the plant more of what it wants, but if your slope doesn't have shade, it won't be as aggressive.
So if you are looking for a groundcover that survives even when it doesn't get what it wants, this plant has worked in my garden. Yup, I am working to get it out from under the tree and out from under the rose it is moving towards. Note: Both the area under the tree and the rose get more regular watering, that is why the plant is moving towards those areas.
It's a possible solution.
Smiles,
Lyn
