I'm a bit slow on the uptake - but I think the Sony engineers slipped a bonus into the design of their power supply for this PCDP. The Sony D-EJ2000 includes an external battery pack using an 1.5V AA battery, in addition to the internal 1.2V NH-14WM gumstick battery. Earlier, I reported that the battery pack has the odd effect of charging the gumstick battery when both power sources are used together.
A couple of weeks ago, I realized that it might be possible to get more power through the headphone out by using both power sources simultaneously - it turns out that my theory was correct. Basically, it makes external headphone amplifiers redundant for this player - you can drive headphones with impedances of 16 - 64 ohms without too much difficulty by using both batteries. I don't know if you are actually getting a full 2.7V of power, but there is certainly an improvement from using the stock internal NiMH battery.
This design might also translate to other Sony PCDP designs incorporating external battery packs, although I wouldn't expect much of an improvement in sound quality from players using digital amplifiers.