It is ~$11 more for a solid filament specific TX from Radio Shack. The 12.6-0-12.6/2A would get run full wave with a pair of Schottky diodes and CRC filtering to deliver the 12.6 VDC to the filaments at a half an amp. RCRC might be better as the charging events( spikes of current delivery to the capacitor at the peaks of the voltage wave-form ) of the first capacitor can spread themselves around and make things a bit dirty.

I have tried AC on 5687 and while I get close to tolerable hum it never quite got quiet enough. It is 4x the current delivered to a 12AU7 and that valve is just able to run a llinestage on AC( with a lot of care, see the Bottlehead efforts in that arena ).

I had specified two heater windings to offer maximum flexibility for rectifier choices, not to run the ampifier's DC filament supply. I am sorry if this was not clear before. It saves a bunch of headache to keep the filament and B+ DC supplies as seperate as is possible.
regards,
Douglas