Valve heater voltage without separate windings
It's possible that the TV put all of the heaters in series directly across the AC line input. Very common in cheap "hot chassis" designs.

There's no reason you couldn't add a second power transformer yourself. 12.6 VAC transformers are very readily available.

Or you could use a separate DC 12V supply for testing purposes &mdash; Heaters don't care whether they're getting AC or DC.