As an overview, the Raven is a 1-stage amplifier with a 4.5:1 step-down transformer, and is output-limited by what both sections of a 6SN7 can crank out. The Blackbird is a 3-stage amplifier with a 28.7:1 step-down transformer, and is output-limited by what a pair of 300B’s can crank out.
The ideal solution for planar headphones is a 2-stage amplifier. For example, in the xDuoo TA-10R headphone amp sitting right next to me, a 12AU7 followed by a pair of Class A emitter-followers for each channel. Simple and inexpensive. Or, small power amplifiers in the 2 to 5 watt range ... all transistor, hybrid, or all-tube. The all-tube solutions ideally use step-down (output) transformers to match the load to the capabilities of the output tube.
Vacuum tubes can swing lots (hundreds) of volts, but are current-limited by peak cathode emission, typically measured in tens of milliamps, not amps. Bipolar and MOSFET transistors, in contrast, can pass not just milliamperes, but several amps, which is why they can be direct-connected to low-impedance devices like 8-ohm speakers and 20-ohm headphones.
A quick note on transformers: the voltage/current transformation ratio is the same as the turns ratio, but the impedance ratio is the square of the turns ratio. For example, the output transformer of the Blackbird, and many other other push-pull amplifiers, has a primary impedance of 6600 ohms, and a secondary impedance of 8 ohms. 6600/8 = 825, and the square root of 825 is 28.7228, which is close to the physical turns ratio. In a well-designed transformer, total losses are less than 5%, so can be neglected for this calculation.
So the output transformer of the Blackbird multiplies the peak current of the 300B pair by 28.7 times, offering peak currents of several amps to the loudspeaker. Similarly, the output transformer of the Raven multiplies the peak current of the 6SN7 by 4.5 times, which is plenty for driving a cable, but not really enough for planar headphones which mimic loudspeakers in terms of current draw.