A couple of rules:
1. A tiled layer with a different spatial reference than that of the map will never display.
2. The first layer in the map defines the SR (unless SR was explicitly defined at startup) for the lifetime of the map (exception: See #3)
3. Once an SR for a map has been set, it cannot be changed unless you clear the entire Layer Collection, and either set the Extent to null or an extent with the new desired spatial reference, then add the layers you want (if you set the extent to null, see #2, else see #1).
So to make your code work after calling 'this.MyMap.Layers.Remove(tiledLayer)', set the map's extent to null (note however that this will only work if the tiled layer is the only layer in the map. If not, you will have to remove all layers first)