Chipping in very late ....
but there seems to be different ways of testing, related to different points on the performance curve. I grew up with Williamson's suggestions, apparently adopted by a number of manufacturers. OPT inductance will rise with level, thus it was adopted that the lowest level of meaning is 5Vrms into the primary. A leakage reactance standard test seems to be with a signal of 1 kHz, output shorted obviously.
For frequency response of the transformer itself, the OPT must be tested under operating conditions, i.e. the input feeding impedance must be Rl in parallel with tube rp. E.g. for a p.p. EL34 with screen taps, rp seems to be close to 3K per tube, with Rl 6,6K, thus equivalent feeding impedance some 3K over the plate-plate terminals. The secondary is then loaded with the loudspeaker impedance, typically 8 or 4 ohm. A sweep over some 10Hz to above 150 kHz is advised. I prefer manual sweeping as one can advance more rapidly over the flat middle range, and fine tune in the upper h.f. for possible peaks indicating resonance accompanied by phase shift, of importance to later sort out negative feedback stability.
Obviously testing for maximum power (some point near core saturation) and distortion is also informative but requires instruments not generally available to the experimenter.
I hope this is not too old hat; I did not carefully reread the whole thread. In my half-century of designing tube amplifiers I usually found the above sufficient. Other matters rather also involve the electronic design and finally depends on that. (A word of 'sympathy': The poor OPT is often singled out as THE culprit in tube design; I have often found sloppy electronic design as much to blame.)