The 3S4 cannot produce much signal current, so lowering the source impedance with a cathode follower still won't drive a headphone well. To get useful headphone output with just the tube, you need an output transformer, matched to the headphone impedance.
The popular Quickie/Speco combination will generate about 1mW into a 300 ohm headphone but only 10%-20% as much into a 30 ohm load - 7 to 10dB less. Using parafeed you can increase that to four times the power (another 6dB), but in addition to the choke, the Speco will now need to see 600 ohms optimally, and the operating point would have to be adjusted a bit.
While I have a transformer design in mind for headphone amps, it's not likely to materialize until some current projects are in production. Meanwhile, if anyone is interested, look around for a transformer with an 8K primary (I think 5K to 10K is a reasonable range) and a secondary matched to your headphones.