Looks like fescue in those pics is what you have already.
Fescue is good in that it's does well in not as much direct sunlight but requires more water than a Bermuda, it also can pretty easily be regrown by throwing seed down.
I'd suggest aerating your lawn, then spreading a top soil with maybe some coarse sand mixed in with it, use either a push broom or a rake to spread around your yard, this will fill in the holes the aeration creates, then spread seed, water and cross your fingers.
Should do the trick though.
Ah, thought I read TN not TX at a glance, gonna be St Augustine then.