tall fescue grass is cool weather grass. It will never survive hot summers here in Texas!

You might as well give up trying to grow grass there. Put wood chips around the tree unless you want to cut the tree down. my mom has magnolia tree and it isn't very big but there is bare ground directly underneath it.

Another option is to grow Liriope muscari in the bare area. Make sure it is MUSCARI, not SPICATUM!

Here is a link that might be useful: Liriope muscari

You might like the look of Irish Moss. It could actually turn out looking a lot like a putting green if it will grow Texas where cool weather grasses supposedly don't grow.
Despite what the NTEP trial ratings say

Also when did you plant that shady mix seed? IF you did it in the summer, it's no wonder it died. You need to sow that seed when soil temps are lower. Such as in the fall. Then give it several months of root growth before the hot weather. OTherwise it can't handle it. If at first you don't succeed...

Grow a shade garden or shade tolerant ground cover because no grass on earth will grow in your conditions.