Have you tried running your app from the local system, and if so, is the result the same?
I copied the project folder locally and same result when open in VS
It seems like it is the wizard that is referencing the System.Core dll from the AutoCAD folder because if I create a new project and reference the AutoCAD dlls (AcDbMgd and AcMgd) manually I didn't have the same issue of ambiguity. But if I use the wizard I see this issue.
At this point I just want to not reference the System.Core dll from the AutoCAD folder because I shouldn't even need a reference to it and I don't want to have to recreate the project because I have a lot of forms I would need to recreate and code to make sure is correct again.
This is starting to get frustrating because I can't find the reference anywhere and I don't see why it would be referenced in the first place with the wizard?
I don't use the wizard so I can't tell you much about what it is doing, but my guess is that the reference is indirect (IOW, one of the Autodesk assemblies referenced by your project references the file in the AutoCAD folder).
And, it is probably not AcMgd or AcDbMgd, it is most-likely one of the assemblies that is dependent on WPF (like AdWindows.dll), so unless you referenced all of the assemblies that are referenced in the problem solution, you might not see it.
[Update]
Here is something that may be worth a try: If your project contains references to any assemblies located in the AutoCAD program folder (and are not in the SDK folder), try copying those assemblies to the SDK folder, and reference them from there (CopyLocal=false). Because System.Core.dll is not in the SDK folder, the Autodesk assemblies that are referencing it should use the same one that you're referencing.