Thankyou, as I thought, the "L(pri)" in equation (B) of post #3, and the "Lp" in the equation (A) of post#3, both refer to the inductance measurement at the primary with the secondary open, and not the primary magnetising inductance.
By the leakage measured at the primary with the secondary shorted, as you know, this measures both the leakage in the primary , and the secondary........the measuring tool will see the secondary leakage inductance as if it were in parallel with the primary magnetising inductance, and it will "see" this term in series with the primary leakage inductance component.