Interstate 20 and 65 instead of Interstate 30 and 40?

First, there is no reason to avoid BHam unless the construction for the I-20/59 / I-65 interchange (also known as the "mix-master" or "malfuction junction") has begun. Then, if you just want a detour around the construction, there is an efficient one - take exit 123, turn left, go approx 1/2 mile and turn right on Finley Blvd. This runs into I-65 just North of the interchange.

I wouldn't recommend Hwy 69 as a detour. That will take 4 hours and all you will see are old coal mines. Not very picturesque!