[Tobiah]

I set the headphone amp volume to max, and controlled the volume from
the device itself - my iPhone.

You run the risk of bring up the iPhone's noise to an
audible level. I would listen to the iPhone with the
volume down but the amp cranked up to see if you can
hear any noise. If you can, bring the amp volume down
until you can no longer hear the noise, then see if you
can get a comfortable listening volume by raising the
iPhone sound level.

Tobiah