converting inductance to electromagnetic force
The force per solenoid inductance is not calculable. The reason for that is that the external force generated by a magnet depends only on the external field, whereas the inductance depends on the number of turns. Inconsistent units before you start,

However, there is a very simple relation for magnets generating force.

If a magnetic field of B Tesla exists in a space between two pole pieces, then the pressure between those pole pieces is 4e5*\$B^2\$ Pascals, that's about 4 bar, 4 atmospheres of pressure for 1T. (You can calculate this figure by using the energy variation method, how much extra energy is stored when you create new volume by drawing two pole pieces apart with a field between them, force is delta(energy) per distance, and the figure is actually 1e7/\$8\pi\$)

This tells you why those electromagnet hold-closed door locks are so effective, a magnetic field of 1 Tesla is trivial to generate when the iron circuit is complete. That also tells you why they are so weak at pulling when there is an airgap, because you need a lot of current to push a decent field through an airgap.

Now you know what pressure you get from an external field, you just need to calculate what the external field is for any airgap length and winding geometry. For a small airgap in an otherwise high permeability circuit, the field B is given by B=\$\mu_0H\$, where H is in units of amp/metre, or turns*current/airgap_length. If the airgap is large, then you have to do 3D integration, or use emperical approximations, not nice.