They make them but they sure are expensive. Here's one. Be prepared for sticker price shock.
5th Wheel Power Mover Electric Powered RV Transformer Trailer Dolly - 15000lb Capacity
www.saferwholesale.com
If you only have to do this a few times (maybe even just once?) maybe you could take a page out of my dealer's book. When I was there last they were using a skid loader to move RVs around. Most of the mid-sized and up ones are strong enough to do the job, and they turn on a dime so they're easy to maneuver in tight areas. They can be rented for 4 hours at a time from most big box hardware stores and rental centers, and if you got one with adjustable forks you could probably figure out a way to temporarily chain your hitch onto it. Some plywood would protect your grass. This would be incredibly dangerous and I 100% do not recommend attempting this (but it's what I'd do...)
If you do, make sure you Youtube it