It almost sounds like the McCormack has some type of auto-sensing gain control, but their web site and the reviews mention nothing about that. The noise doesn't really behave like any defect I've seen before, but maybe that's what is going on. Only further investigation will tell.
However, Stereophile's review of the DNA-225 did have an interesting comment
Too much system gain can aggravate noise problems. Stereophile also tested the amp's S/N ratio (though not your model) and it wasn't as good as published specs.
If no defects are found, it is looking more and more like you have two wonderful pieces of equipment that simply may not be suited for each other.
However, Stereophile's review of the DNA-225 did have an interesting comment
"The voltage gain into 8 ohms was higher than usual, at 30.5dB. Both of these factors will make the McCormack a good choice for use with a passive volume control, though pairing it with a typical tube preamplifier will result in too much system gain."
Too much system gain can aggravate noise problems. Stereophile also tested the amp's S/N ratio (though not your model) and it wasn't as good as published specs.
If no defects are found, it is looking more and more like you have two wonderful pieces of equipment that simply may not be suited for each other.