There’s nothing that really covers sliding the core around because inductance is generally a measured not necessarily predicted value. The exact geometry impacts inductance so you want to test at the end to be sure
What you’re going to end up with is something partway between an air core and an iron core inductor.
Iron core inductors have higher inductance values in the same size, higher losses due to core losses and eddy currents, and if you run too much current through them you’ll max out the field the iron can support and saturate the inductor.
Air core inductors have lower inductance, lower losses, and cannot saturate.
Moving the core in and out is going to change the inductance significantly and potentially cause it to saturate depending on the current levels
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