I'm just guessing but the east-west might have been named something like Byram's Ford road.

There are two roads shown north/south to the east on a map in Monett's "Action Before Westport 1864". The first (westernmost) running due south from Westport is Wornall's lane, the second is Harrisonville Road (crossing the Big Blue at Hickman Mills.)

Hope that helps. I imagine local historical societies might have some area maps predating 1900 that might help or confirm names.