• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

What's This Formula Tell You

So you have HD-569?

Really loving your headphones is helpful, because you could build the amp around that specific pair.

The Sennheiser specs say that those get really effing loud off 1V RMS, so we can establish that as the goal at the output of the transformer. We would also assume that you're going to plug your phone into the amp and expect it to drive your headphones, so we need to go from 0.3V to 1V. Based on the gain of the 6DJ8, you're then best off with an output transformer having a 10:1 step-down ratio.

The 10K:150 Edcor is about all I see that's in the ballpark. It won't quite reach those ambitious goals, but you could plug your headphones in between the CT and one end of the secondary winding and you'll be in the ballpark at least.
 
...You could add some series resistance between the 75 ohm tap ....

I don't see this mentioned in all the verbiage: The center tap of a 150r winding is 37 Ohms not "75".

> searching for the same data for the 6DJ8

The DJ was NOT sold as a power tube. It is the first stage in a TV set, to pull very weak signal off the antenna and boost it gently. IMHO it is not a good choice for a headphone amp. (I have done such a thing with a similar tube, but when they were $1/each.)

Some 6DJ8 data does not show a Plate Resistance, because in a TV tuner it is not a primary design factor. (The tuned circuits at 100+MHz are even lower resistance than the tube internal resistance.) You can work it out from Gm and Mu. (About 2.6k at 15mA.)

The happy load of a tube is complicated. For triodes, for our purposes, we find the Plate Resistance in a datasheet "typical" (show-off) condition, multiply by 2X to 5X, and find a transformer to lever our load about that value.

The proposed plan is push-pull. Double the load for a single tube. (No, it is not that simple, especially if reaching for MAXimum power, but in this case just close your eyes and double it.)

2X makes more power but more THD. 5X makes less power and THD. Many headphones never need as much power as even a small triode can deliver, no strain, low THD, so it is NOT critical.

The 10kCT:150/37 transformer, with 21r on the 37 tap, will throw about 2.8k load on each triode. This is close to 1X Rp! This is more tolerable in push-pull than it would be in single-ended. In some simplified theory, Rl=1X*Rp is "maximum power", but only with a lot of restrictions.
 
so the lm334 only needs 0.68 volts half of the lm317....

lm317 datasheet says a minimum of 3v between Vin and Vout and a 10ma minimum current.
lm334 datasheet says 1v minimum between Vin and Vout (at 5ma, lower at lower currents) and a 10ma maximum, but you can parallel multiple devices for greater current if needed.
A J505 has a 1v minimum and gives 1ma of current. Parallel multiple as needed. A J508 has a better temperature coefficient (less change in value with temperature) and does 2.4 ma, but needs 2.2v minimum.