Two problems with that are (1) getting from the C&O to Front Royal, and (2) this routing will involve some E-W overlap. For #2, you'll have to decide how you want to get south towards Orlando from not-Washington; one possibility would be to catch the Adventure Cycling TransAm from Rockfish Gap towards Charlottesville, then take the Atlantic Coast south. If you like the hills, you could tke the BRP down south of Asheville, NC, and head southeast from there.
Re: #1, you've got three or four choices. You could cut south from Hagerstown along (parallel to) U.S. 11; go south from Harper's Ferry; cross the Potomac at Brunswick; or take Chain of Rocks bridge through Leesburg, the W&OD to Purcellville, then southwest. I've only taken the 11 route before they finished I-81, but there's a fair few towns with way too much traffic for my liking. U.S. 15 from Chain of Rocks to Leesburg is narrow and winding, but still a long way to go on that kind of road on a bike with more traffic than I like. Somebody else will have to discuss the other two routes.
You might reconsider going into Washington, although it'll add a day or two. You can go into D.C. on the C&O with only bike, jogger, and walker traffic, cross the Potomac (0.5 mile or so), and then leave D.C. in Virginia on the W&OD out to Purcellville, very much like the C&O except with a handfull of road crossings. In between you have some great restaurants.