> what am I doing which is so stupid?
Nobody else here seems to think so, but I think the AC voltage for feeding regulators should be the DC voltage plus 3V. So you want 9.3V windings.
> 30VA with 2 x 6V secondaries. ...a bridge rec ...I get 8.4V unloaded. {loaded} bridge rec drops to about 6.7V and the max I can get out of the reg is 4.5V.... max current draw is something like 2.6A on start up settling down to 1.6A in normal operation.... for ref http://www.national.com/ds/LM/LM150.pdf
The 8.4V is "perfect" (6V*1.414), meaning it can't be that high with any useful load. I would expect no more than 7.2V (8.4V-1.2V) with any significant load. And you are already in trouble, because the in/out drop of a 350 at a couple amps is a couple of volts. Add in some ripple, you are down to like 7.2V-2V-0.2V= 5 volts maximum clean output. Less on bad days (when utility power lines sag).
Why do you need regulated? If you actually need 6.300V, you better have a LOT more headroom on that regulator; their regulation sucks when you push the in/out difference too small. You would not starve your audio amps and pretend that 0.1dB headroom is enough, why do that to your regulators? Stick about 10VDC on the top of the 350 and damm the heat.
Or... since you have the 6V windings already, and tube heaters do NOT need regulation on any semi-civilized utility power, just get passive. And since you have 2x6V, don't use that silly bridge and its double-diode losses. Wire the windings in series, ground the center-tap, run one diode from each hot end to the filter cap. (You can use the bridge-rec you have, just use 2 of the 4 diodes, the two that go to the "+" pin.)
You should get 7.8VDC at light load. You need to have enough first capacitor, and at these low voltages you want MUCH more than 1,000uFd per Amp, or much more than 2,000uFd, possibly more like 20,000uFd for minimum ripple and maximum average DC. (But 6,800uFd isn't bad.) The 7.8VDC is about 1.5V more than you need, and load is about 1.5A, so stick in a 1Ω resistor and a second big cap, 6,000-20,000uFd. Ripple winds up around 0.1V to 0.01V depending how big the caps are.
And this is true no matter how the wall-power varies, whereas a starved regulator may be dead-clean on high-line days and total ripple-crap on low-line days. Heat in the resistor is obviously the same as heat in the regulator (if the reg could work at such low voltage, which it won't), and a 5W resistor can run hotter and be smaller than a sillycon chip and fins. You won't get 6.300V exactly, but (assuming no mis-wire) it will be close enough to make the tube happy. Let it cook with a voltmeter on it and see if it tends to be high or low when fully warm. Use 10Ω parallel or 0.1Ω series resistors on the 1Ω resistor to fudge the heaters into the 6.1V-6.3V range.