Somehow, having had great experience of using PL504s in TV applications, using such a huge component to drive a 600R headphone seems like massive overkill. The tube heater alone consumes 10W of power and lets say another 1W of anode power and all it does is provide about as much audio as a 741 op-amp! Paralleling them will indeed drop the impedance but even with FvM's quoted fourfold power increase, it will be extremely inefficient. Each PL504 will add about 11W to the PSU load but only a few tens of mW of output power.
To reach 8 Ohms impedance in that schematic you need to parallel 75 tubes so you would be looking at some serious forced air cooling to get any appreciable sound from a speaker.
Brian.