I don't know if this matters to you but yet another consideration is that there probably won't be very many leaves on the trees in March and early April, which IMO greatly detracts from the views. You also won't encounter many other riders with a March start.
OTOH, when there are no leaves on the trees, you can see out almost anywhere when you get into the mountains. Wait until May, and you can't see the valleys below until/unless you get to an overlook, power line, or some other break in the trees -- at least in the Appalachians and Ozarks.
Just MHO, but early March is likely to have tough weather, mid March is a crap shoot as regards the weather, and by late March (or by the time you get into Kentucky, if you leave from Yorktown), you'd have a pretty good chance at tolerable weather. Fronts will come through, and you'd do well to plan to hole up for a day every week through April, but it'll be cool instead of hot and sticky the rest of the month.