We did the trip in October of last year.
Did not take the coach on the parkway. We moved the coach to a campground and used the toad to travel on the parkway, doing about 100 miles north one day and then 100 miles south the next. Did not have issues finding campgrounds and driving the car was more relaxing and scenic for me the driver. We usually made the return trip to the campground off the parkway. Worked out well for us. We started at the north end of the Skyline Drive so we could see both.
We did run into snow at the last stop in Maggie Valley and the parkway was closed for 2 days. We missed being snowed in, in Boone NC but were leaving for Maggie Valley that day.