What you want is to dynamically scale the camera so you can only see the map. This can be done by passing a different projection matrix to the SpriteBatch:
var graphics = /* your GraphicsDeviceManager */;
var width = graphics.PreferredBackBufferWidth;
var height = graphics.PreferredBackBufferHeight;
var windowSize = new Vector2(width, height);
var gameSize =...
While I have spent years working with XNA across Xbox 360, Windows Phone 7 and PC, this kind of a problem is typical and requires lots of tedious configuration of the target system.
While I was once successful in past, it took more effort than to simply update graphics API (say, DX8 to DX11).
Every new version of VS links against different libraries. Given ...