Method for inductance measurement of iron core vacuum tube audio output transformers
Just off the cuff...


Measure DCR of primary and secondary and after max Vrms/Z(f)=I with load is known, you have I²R in both primary and secondary.    
Measure Lp/Ls to compute n² turns, voltage ratio.
Measure Output Impedance with primary shorted using known source impedance to measure V drop and thus Zsc. 


This can also be defined with the rated, Zr[Ohms] = [Vrms]²/[VA] 
then Z load/ out is your dampening factor for the lowest bass f of interest with cathode Rc/n² added to Zsc in series = Zout

Measure impedance by increasing both I and f as Eddy Current losses increase with Pec = k * (I*f)² by measuring impedance drop  at 10k or 20kHz with rising current.  This will not be just a fixed shunt R as EC losses are not constant.


If you don't have a Sig Gen , use Audacity.  
Good CRGOS Silicon Steel with Silicate insulated lamination gives the lowest hysteresis 
Bsat threshold for inductors and transformers is usually defined by 10% drop in L with applied V, but using a primary short circuit and driving the secondary is easier with a low power Amp and sig gen input.  ( I think .hmm)



If the Laminate is good M6, the core losses can be less than 1.5W/kg at 50 Hz.  Any interlayer shorts can reduce the overall core capacitance but also raise the B level closer to saturation.

I'd be very impressed if the transformer spanned more 3 decades in frequency with a flat response. I don't ever recall seeing any. But this could be a first with greater laminate gaps and lower mutual coupling.