I guess I will put out something of value -
Simplest lightest bike that will do the job is the trick when it comes to ease of touring that involves serious single track and unimproved roads, getting in rutted root crossed paths, and other crap.
If you want to make it some challenge to prove either that you can do it or that you're just plain foolish - or both - then do something goofy like some have mentioned. Ride an R1 across the desert and snow covered tundra, do it with a Wing or a Road King. After all, you can also motocross race a Harley or Gold Wing too, if you want and the promoter will allow it...
Oddly enough a CX500 actually makes a bit of sense - ever see how much ground clearance they have? Makes some adventure bikes jealous! I swear it had to be about 10" or more! Some good shocks and forks along with dual sport tires would put that bike firmly in the Adventure bike class.
18 or 19" front wheel, stock forks and shock length close to stock, and the bottom of the engine is nearly in-line with the axle centerline! That's ground clearance.