Tell me more... I always thought the "magic" was in the original conversion. Are you saying that you can take an electronically balance signal and impart the warmth of a transformer balanced signal at the output of the device?
Transformers don't know or care if the signal they are getting is electronically balanced or not. They also don't know if their secondaries are generating a balanced or unbalanced output. Transformers live in their own world, referenced only to themselves. All they know is the difference in potential across their primary coils, and the source and load impedances on each of their coils.
The 'magic' in a transformer is a property of the transformer itself. It tends to be a function of the signal level; in other words, hit the transformer hard if you want it to saturate.
If we step back a bit in the history of the transformer and its modern application, we'll realize current techniques are a bit odd. Transformers originally were a part of audio gear because they were really needed for impedance matching (and of course excellent CMRR, which they still provide). Manufacturers strove to make their transformers as linear as possible, which since they had to cope with the hot levels required for tape recording meant really big, expensive transformers.
With modern solid-state gear, impedance conversion is not required. Also, transformer design has been raised to a high art by companies like Jensen. Operating levels can be far lower, because converters don't really want to see +20dBV, most clip internally at +6dBV or less, and have to have "pro" levels padded down to a level they can tolerate.
But still, the saturation that the designers of old and the modern masters try so hard to avoid is viewed at desirable. And so people need to push very hot levels into low-distortion transformers to get them to saturate, and then pad down the transformer's outputs back to a tolerable level.
To me, it makes a lot more sense to select a cheaper, smaller transformer that saturates easily and get the same effect at 0dBV . . .