I have a constant filling that my DT880 (600ohm) would benefit from extra power (at least 500 mW).
Passport says, MKIII delivers 350mW on 300/600ohm load. Looks like this is the minimal requirement for these headphones, as I have to push my MKIII to the limits from which the hiss noise starts bothering me (80% on gain 10).
There is something weird about it.
I do not know output power of your source, but mine MK III loaded with 6H6P-I is currently set at 20% while my DAC (E-MU 0204) volume is set to 90%
If i were you, i would check mine gain settings and then inspect your souce.
Because if amp is on gain 10 running at 80%, your source must be giving incredibly small audio output.
My MK III runs at 80% when i set volume on E-MU to 10% and still not so much noticeable noise btw...