How can this inductor I built (picture in post) have such a low inductance?
In my limited experience the air gap in a home-made or reassembled core is much bigger than the original, and the performance is much lower than you think. To achieve effectively continuous iron, the laminations are precisely made and held pressed tightly together by the corner bolts, or glued while in a large press to eliminate air.
Better to cut off the old winding and re-wind by threading.
If the iron has a relative permeability of several thousand, then an air gap of 1/1000 of the core path length will dramatically lower the effective permeability and inductance. This would only be 0.1 mm in your case, or just a few sheets of paper worth of air or glue at each of the many joints. If you need glue to hold the laminations together, and didn't compress the core while it was setting, that's the most likely problem.
Work out the inductance you'd expect with a soft iron core, but with a 0.1 mm air gap.
Well done on your various measurement techniques, they sound like they're reasonably accurate.