@valleylynn,
I'm unsure what the makeup of the soil under the tree is, but here's a picture (it seems kinda sandy/kinda "soil-ish"?). There's some perlite in the picture, but I'm pretty sure that was from me ripping out plants. I believe there's some clay once you go deep enough, but I don't dig too deep considering the tree roots (sorry, there's some mulch in there).
Here's a picture of the area. I mulched to *maybe* an inch thick. There's really not that much mulch, that's about as much as my edging will allow. I'm not doing anything with the outside "circle" (so ignore all that dirt and bits of mulch, I'm going to turn that back to grass

).
Loooooottsss of sun, all day. Afternoon sun is more brutal on the backside of the tree (closest to the house). The tree, when in full leaf, provides no protection at all from the sun (so no to filtered light).
I think the tree is about 15-20 feet tall? I'm not good with measuring! :confused:
Winter and Spring seem to keep the ground pretty moist, would that be an issue for a Sedum? It's when we hit Summer temperatures (90+), I have dry, dry ground.