I can't find a map one around here. they're apparently all in the coach.
If 48 is Briley Parkway, you can avoid some traffic. It makes for a circuitous route, however. Lots of people would like to avoid Nashville. there ain't no way all routes go within 30 miles and it's all more of a mess than we want. There is US 31, from Lebanon area, or rather still Nashville congestion, north and US 27 also to the east, of Nashville, very east as in Crossville. Other side through land Between the Lakes and some rural and tiring routes, way to the west, of Nashville. Might work out a route from I65, 840, to I40, west and through Land Between the Lakes. Stay away from Jackson.
Sounds like you got it more figured out than I would anyway.