"E88CC style" is not sufficiently specific - the 6DJ8 variants cannot handle enough plate voltage, though the 6922 types can. However, all of these tubes really want more current to operate properly, and with enough current they are likely to exceed their dissipation limitation.
To get the hum down for headphone use, you must rectify the 2.5v filament power (one for each tube). Doing this is more difficult due to the high current, and voltage losses in the diodes. There are other ramifications, but this is a post, not a dissertation!