I’ve looked at my route options before. I’d love to find a non-interstate option from west to east acrosss TN. It could be done, but probably pretty impractical and would add a ton of time.
Look at US highway 64- - - - -it runs from Memphis to Chattanooga and points east from there, right along the Tennessee/Alabama state line. It's a divided 4 lane most of the way, with some very nice scenery and lots of possible side trips. I live about 5 miles south of 64, near I-65 and the Alabama line. US hwy. 70 eastbound from Nashville would be another non-interstate option.
Jerry