Thanks for those replies.  Those are some thoughtful responses.  As for the hitch rating, I haven't eyeballed the rating, but the brochure says it's 5,000/500.  This is a Class A 2020 Winnebago Intent.  It is built on the Ford F-53 gas motor chassis (not a bus chassis) so I call it an A Minor (music humor).  
A 4-door Jeep Wrangler Unlimited weighs around 4,500 from what I've read so I would be near the tow limit, and I still need to weigh this loaded to be sure I'm under GAWR and GCWR limits.  I was thinking maybe a 2-door Wrangler due to weight limits, but I do like the 4-door.  As for the motorcycle I hadn't thought about how a road bike performs off road.  That's important to know.  I had also thought of towing a 4X4 truck with a motorcycle in the bed, but that's probably over my weight limit.