Output Transformers, why are they made like this?

[boater sam]

If you're seeing blackened windings, I'd suggest it's down to insulation failure, and a steady (and high)  drain from HT+ through the breakdown, to the core.

Which is why I considered winding the primary on the outside, away from the core.  The potential difference between the core and the secondary will be negligible.

 I'm going to try it at my next winding session.