To answer your question Todd, my quietest tubes are GE, but I would guess that noise is more variable tube to tube than brand to brand.
One other thing I was thinking about, have you put shorting plugs on the input to rule out noises from outside the amp (source, cabling, et cetera)?
One question I have for the group, the headphones in question are 118dB/mW. Assuming my math is correct (huge assumption) that means a nanowatt would produce noise of about 60 dB. Is this asking too much of the circuit?
In regards to the 120Ω resistors, would it be feasible to put them into an inline headphone adapter? This especially would make sense if they were terminated with a 1/8" plug and you needed an adapter anyway, but even a 1/4"->1/4" that you only use with the phones in question might make sense.