I'm in Zone 8b (right at the edge of 8a); Southeast Texas

My front garden bed is a struggle. It faces southwest and contains a crepe myrtle and a red oak. The oak tree will not lose all of it's leaves until early spring when the new leaves start coming in. It currently has ligustrum planted between the two trees (slow growing but otherwise okay) and loropetalum planted in a half circle around the trees. The loropetalum is doing very poorly (this is an older photo, it looks far worse now). Each side has at least one dead plant and the rest are halfway in the grave. I'm pretty sure they're not getting enough sunlight.

The loropetalum needs to be moved and I am open to moving the ligustrum. I need this bed to be easy to care for. I don't want to be constantly dealing with weeds. Could ground cover be the answer to my woes? If so, do you have recommendations? Ideally deer resistant. The bed gets partial sun, but in the summer it's an intense sun in the afternoon.