6.3VAC * 1.414 bridge - 1.414VDC rect losses - 1.5VDC reg dropout = 6VDC, just a tad low
The "low" is a total non-problem. But you have neglected to account for ripple. If a DC meter reads 7.5V into the regulator, and you have 1V p-p ripple (not an unlikely value), then you will have -0.5V pips on your "6VDC" output, which totally defeats the purpose of a DC heater supply (those pips will contaminate all the audio).
Agreed, and this is interestingly, a rather common mistake.
If your heater supply is overdimensioned and you really MUST regulate it (see below) you may want to use a voltage doubler to get around the dropout problem, but it's still a crutch.
Tube heaters do not need regulation... Take your AC, rectify, put in a BIG cap, a low-ohm high-watt resistor, and another BIG cap. 10,000uFd at 10V. A big C-R-C filter delivers smooooth power. Fiddle the resistor to get 6.0 to 6.5V at the heaters.
If I may add something:
People tend to forget that tube heaters are not resistors. They are nonlinear and to an extent are self-compensating: Lower voltage means lower temperature means lower resistance means higher current means more power means higher temperature.
If this were not so, series heating would never be possible.
Regarding the CRC filter mentioned above, I would actually make it a RCRC filter. The problem with rectifying low voltage and high current transformer windings is the need for very large capacitors, which in turn decreases the rectifier conduction angle, and increases the peak rectifier current. This in turn does two things which you REALLY do not want:
1) The reverse recovery time lengthens because of the higher forward current, resulting in 'inexplicable' overheating of the rectifier and filter caps. This is often 'solved' by fast soft recovery or schottky diodes.
2) The high current pulses generate substantial magnetic fields from the wiring and especially from the transformer as well. They can momentairly saturate the transformer at which point they become a stray field. They can and do also bleed through other windings to other power supplies, especially if a toroidal power transofrmer is used (remember that other rectifiers conduct at the same tim, probably with a larger conduction angle). Since the pulses are very short, their high order harmonic content is very high. Fast recovery or schottky diodes will actually make this worse, often producing HF hash into the MHz range. Self resonant transforemr problems are also possible, as damping is relatively low, since the caps, rectifiers, and winding all have low resistance.
A simple resistor in series, before the first smoothing cap (and you will be dropin voltage on a resistor anyway so no big deal) will widen the conduction angle, reduce peak current (often dramatically) and very cheaply solve all of the above problems.