Jeremy,
You can stop looking into this issue. I found the solution. You were on the right track though, even though that didn't ultimately help me find the solution any sooner. Whille having a space in the URL worked fine in 2015 and not on 2016, replacing the space with a pike "|" symbol works on both versions. I found the answer within the Revit 2016 SDK, which includes a Revit Viewer example written in C++.
This is the working 2016 URL to get the contents of the root
http://RevitHost/RevitServerAdminRESTService2016/AdminRESTService.svc/|/contents
I genuinely do appreciate your time and effort to help solve this. However, at the same time, I did not appreciate what I perceived to be hints of condescension masked with pleasantries within your replies. Perhaps I am reading more into it then was there... but I doubt it. It seemed pretty clear to me. I'm sure you are a smart guy Jeremy, and are much more knowledgeable on certain select topics than I, but it would serve you well to check your ego at the door when helping the paying customers of the company you work for. You've taken what could have been a positive interaction with Autodesk, and made it much less so. You may not have crossed any major lines, but I'd still call that a loss for the day on behalf of your employer.
Ted