Tibouchina tree is what I believe your tree is. I grew ajuga groundcover for years near my pool. It fills a large area quickly on runners like a strawberry, and blooms nice purple flowers in summer.
http://www.pssc.ttu.edu/techho... I cannot seem to put a link in but google ajuga bugleweed. It's a quick growing but not really invasive groundcover, with no brown dead patches, and a small little root system. There is also the succulent iceplant that flowers different colors. May be expensive to cover a large area. I feel like some ornamental grasses would be lovely here. You have a nice start already to this project. Goodluck. It will be fun to see this project complete.
