While I'm not 100% sure this is the case, I would strongly recommend against converting .fbx files to newer formats.
I've been using Skinned models with MonoGame for a while now, and though I haven't encountered this specific error, any amount of minor issues when I export (textures missing, a vertex not being skinned, etc.) will cause a crash. It's possible that converting your model "to 2013" has caused on of these errors to manifest.
My advice would be to re-export your current model into a fresh .fbx without conversion.