[Phlogiston]

That was, at least an attempt at a better transformer. You could wind it with the primary entirely on the inside (conventional). Or you can do it like it was. Sounds like you only need to rewind the outside section, which, I'll bet, was the same value(s) as the inside section. Either way, you will probably not be able to tell the difference.

Some audio transformers were wound side-by-side attempting to get better response.