Thanks jarjarfor posting it!
I have a similar problem, just that I use a disc magnet of radius R and height H.
The Br (Residual Flux Density) is also known.
I've seen that you first compute the reluctance of the magnetic circuit and then you obtain step by step the magnetic flux density B.
In the image below you can see the magnet and the mild steel plate that is pulled, the gap varies from 0 to 0.2mm
To get the magnetic flux density B, I have used eq. (1) and the same magnetic pull force equation as you.