No there is not any good way to avoid those two for where you are going. I-40 to Asheville is not that good of a route plus it's over 110 miles further.
I go straight through Atlanta all the time on I-75 but not at rush hour. Do not stay in the right lane as it will become an exit... even the two right lanes at I-285 (do not use) on the north side and downtown for I-20.
Have to admit that a GPS is handy for getting through Nashville on I-24 so you know which side of the road to be on. It's more complicated than going through Atl.