Not sure what you are looking for. DX image circle is smaller than FX, I believe you know that. If you don't change to DX mode, you'd just get an image circle which you have to fix yourself later.
A 16mm focal length lens is still a 16mm. DX or FX or m4/3 doesn't change the fact that it's 16mm in focal length. It's just the sensor's size's crop factor that changes the "effective focal length", so to say.
So that's why your 11-16mm DX lens is effectively a 16.5-24mm in Nikon FX.
Which means, even though you don't use auto DX mode, you get that pic with image circle and fix yourself and you look at the picture, the FOV is about the same as if you are using a FX lens on 16.5mm on FX mode.