Cheers Kevin - that's great - I have this working on my machine.
As this is a 'normal windows' application (as opposed to windows store app where you set the build action to content) you need to set the png, atlas and json files to "Copy Always" or to "Copy if newer" - see below screenshot.

This then means that the files are copied as part of the output/deployment along with the exe and dlls. The problem before was that they weren't being copied and hence could not load.
I also added the following two lines to ensure that spineboy appeared in the middle of the screen...
skeleton.X = 400;
skeleton.Y = 400;
I put these in the LoadContent immediately after the UpdateWorldTransform()
Interestingly though, taking this approach did not fix your original repository - so there must be something different about the spine-runtime that you built in the original repository.
What platforms are you initially targeting?
If you are targeting iOS (using Xamarin studio on the mac) or a windows 8 store app then there are two spine run-time projects already set-up to do this in the "spine-monogame" folder within the spine runtimes repository. If you look at the folders for these two projects then you'll notice that there are no source files in the folders - this is because they 'link' directly to the source code in the c# and xna folders - thus no need to copy files around and have to worry about keeping them synchronised. Everytime an update to the runtimes is released then I just update these two project files with links to the new source files and then issue a pull request.
If you want to target a different platform (e.g android, or windows (non store app), or mac or playstation or whatever then it would probably be a case of just making another project in the same way. Thus the project files have any platform specific information in them but use the same source code. The only other thing that I've also done is use compilation directives to get round platform specific issues - e.g. see the "#if WINDOWS_STOREAPP" in atlas.cs - required because windows store apps have to load assets in a different way to other .net apps. So it may be a case of creating another project file for your chosen platform. I have not created project files for other platforms because I have only played with windows store and iOS.
Apologies if the above is all known to you already - otherwise I hope it is helpful 🙂
Let me know if anything more I can do.
cheers.
Randolph