• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

Question about SE transformer issue

The culprit could also difference in core properties. If the LCR picks up the main L with parasitic Cp+Cs resonance, main L could vary if for some (BAD) reason the core isn't exactly the same.

P.S. Looks like you, at least partially solved the issue. Quite a huge difference in capacitance, IMHO.
 
Highly possible, yes. Paper varies in density, hardness, all can result in difference of dielectric constant. You should always test your dielectrics before applying them to an audio transformer. pH water test, capacitance test between two plates and dielectric breakdown test, if to be used between high voltage potentials.