I’m not surprised. The great enemy of transformers are high impedance, which decreases bandwidth on both ends of the spectrum, and increased insulation resistance, which takes up room on the winding stack. Both act to increase the size of the core, the winding stack, and the entire transformer.
When transformers get bigger, inter-winding capacitance goes up, and HF bandwidth decreases. Yes, little transformers are better, at least at high frequencies. To get the lows, though, you need more inductance, and that makes it bigger and heavier.
The technique to increase HF bandwidth are more complex interleaving schemes between primary and secondary, but this can cause ultrasonic resonances and poor square wave performance. The art of interleaving has fortunately been somewhat simplified by computer modeling, but there’s still plenty of art involved. You want a skilled builder with plenty of experience with audio transformers.
There ain’t no free lunch with transformers. They solve problems, but you really have to keep impedances low, and work closely with the transformer designer. They’ll tell you what they want, and you tell them what you want, and you work together to meet your goals. In my case, I wanted matched capacitances on the primaries, good phase match at 20 kHz, and the ability to tolerate a certain amount of imbalance current. With SE, of course, it’s all imbalance current, so a (very) large gapped core is required.
A problem with using old transformers is corona discharge where the enamel on the wire has thinned or cracked. Once a point of breakdown occurs, those windings are shorted to each other, and the problem cannot be solved unless the transformer is disassembled and completely rewound using the same interleaving scheme. New transformers are commonly tested with HIPOT, a test fixture that generates 5 kV between the windings and the core.