Using Xamarin on Windows as well. I installed Monogame several times but It didn’t help. Is your default Xamarin project different to mine? Would it be possible to upload a working project 
?
EDIT:
Heureka! It is working now.!
I added a SDL2.dll (win-64bit) close to the .exe file and the program is running.
(Is that normal? -> in: new thread )