That's funny. Reminds me, at one time most of my house was a series of "ledges". Lanscaping was a series of "ledges". My shop was a series of ledges And seriously, that is why I play piano, someplace to set my beer. (it wasn't about the music)
Superbowl 2009 I was at Sloppy Joe's in Key West. I sat my beer on a little ledge that runs around the room. I went to the bathroom and came back. Beer was gone. Got another. Took a sip and put it on the ledge. Lit up a smoke. Turned around to get my beer and it was gone. Looked down and saw two beer cups on the floor. Got another beer and stood there and watched it. About 2 min after setting the beer down, it would develop condensation between the bottom of the cup and the ledge which had a very high polish to it. The ledge was tilted about 1 degree - just enough for gravity to induce motion. And down falls the beer. Makes me wonder if it's by design (to sell more beer). Moral of the story - tilted ledge results in wet floor.
I would put 5/8" particle board or OSB from the floor up to the heighth of the wainscoting, then use sheetrock above that. That way you have a 100% nailing surface. You could trim it out with chairrail where the two meet.