What you described as an "elder care moving manager" is more commonly known as a "relocation specialist," but the concept is exactly the same. In fact, an entire niche market has sprung up in recent years to assist with moves that occur later in life.
One such company, Right-Sized Living, LLC, was founded by Nan Hayes who is actually a Moving Expert at Caring.com. If you go to Nan's website (www.moveseniors.com) you can read more about Certified Relocation and Transitions Specialists (CRTS)and the services they provide. The site also allows you to search for one in your area.