It appears you are as deadended as I am. My sympthy to you.
I have been up against this brick wall for many years and keep hoping I will get "lucky" - but nothing so far.
I think half the Bryants were named William. I know my deadended g-g-father named his first son(though his first marriage) William and following nameing patterns it stands to reason that his father was named William.
If you ever run into some Alabama Bryants in your search with a Thomas J (aka T.J. for Jeff) keep me in mind.