Why is my homemade pulse transformer so inefficient?
The core will have eddy currents, and is not the most efficient
design, but 17% efficiency seems overly low.

Not at all. I believe that most of the coupling losses you see are due to not having laminations. This is why people use laminations or ferrite cores.

The 15 volts on the primary seems to produce a very strong magnetic
field, the pieces of steel are locked together when it is energized.
But this field does not seem to induce any significant voltage in the
secondary.

If the applied voltage is constant then there won't be an induced voltage once the primary current has settled to a constant value. It will settle to a constant value due to the coil resistance.

Am I having massive hysteresis loss?

No, you are having a massive eddy current loss.

What modifications do you suggest to get the output at least above
80%?

Try some ferrite core material or use laminated silicon steel.