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Did you say there is a third 6.3v winding? How many amps is that? If theres only two, it would seem they intended you to hook the two windings in parallel in phase to get the extra current capacity.
It is WAY better to have a separate filament winding floating for the rectifier. If you've got an extra 5 volt winding, you could use a 5 volt rectifier tube like a 5z4. This is a cathoded tube like the 6x5, but the cathode is connected to the filament, so it requires a separate filament winding. Another good solution might be a 5y3. These have a bunch of internal voltage drop, and your dropping resistor(s) would not have to dissipate as much heat.
I like to keep things original though, and so would probably keep the silly 6x5, even on a grounded line if it was the only way.
It seems you have a bunch of windings. What is the voltage of your primary winding? 117? Do you have any primary taps? Whats your line voltage? Mine is 121V.
Heres some food for thought, based on whats currently on my bench. You kinda hit the nail on the head with your comment about the 6x5 possibly having too much filament voltage.
On the old comms receiver I'm currently working on the power transformer had been replaced, and everything was running too high. I had an extra 6.3v winding, probably intended for a damper in an RCA TV chassis. I connected it in series with the primary, phased in such a way to reduce all the voltages. This brought the 5.0v and 6.3v lines back down to normal. The b+ is still too high, but only by about 25 volts. I'm gonna drop that with a resistor.
I would get the filament voltages right, and then do whats necessary to correct the b+. Maybe a winding of some kind could be used in series with the primary like I did, if everything is too high. If a fairly big 5.0v winding was unused, it might run high enough for the 6x5. You can also usually get away with overloading one secondary winding a little if you are not using all the others. If you overload it the voltage will probably come down a little.
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