Possible? Sure. You'll run into several difficulties, all of which are relatively well known. There are solutions for them, though.
The 6.3V/3A winding can be full wave rectified into 6.3V*1.1414 - 1.4V = 8.9V - 1.4V = 7.5V. The actual voltage will be a little more or less, as "6.3V" varies a little in reality. The tricky part is that you don't have enough voltage from 7.5V to run a normal linear regulator to make a stable 6V with a simple linear regulator like a 7806. These things need 2V or so to work right, and the 7.5V estimate is uncomfortably on the low side.
You could simply make the 7.5(ish) and use a resistor in series with the 7.5V to the heaters, with 12A?7 tubes wired for 6V. The resistor eats up the excess voltage. The heaters are a fairly resistive load once they get hot, so this setup stabilizes. Heaters don't really need regulators as long as the supply is fairly well controlled.
There's a lot more to this if you want to dig in further.