Hello Krux,
The recoil permeability is constant (i.e., "straight line") only for SmCo and most high-coercivity NdFeB permanent magnets, because they usually do not have a knee in the BH curve.
It is that knee in the curve for Alnico magnets that prevents one from using straight line behavior. When an Alnico magnet is pushed to its coercive point, it'll follow the path of a minor BH loop that is non-linear. That minor loop will resemble the shape of the major loop, but it'll be at lower values.
It's difficult to say which permeability should be used for your application, it requires a lot of analysis to determine where the magnet is operating at every moment in the cycle you described. It can be done, I remember working through the example in Moskowitz's book, but I have to admit that I would approach it via FEA nowadays.
IIRC = If I Remember Correctly
Best regards,
Mike