Same number of gears in the rear, should be no problem. IIRC the Randonee used road wheels (130 mm) spacing, so you shouldn't need to worry about hub width. Did you take a spin around the neighborhood to test everything out?
The things I'd watch for have to do with tires. Do you have adequate tread life left on the road bike tires for 350 miles? Will the roads be smooth on your tour, or will you encounter chipseal or expansion joints and wish for a bit more volume in the tires?