I really have no idea why the addition of Emotiva's filter created more hum. Did it further exacerbate the problem through some type of interaction with the ADA?

If my theory is proven true, there is definitely something in the design causing the issue and therefore when that design is improved, the issue will go away. Not a good answer I know but the first step is to investigate the theory.

House of the Rising Sone
Out in the mid or far field
Dedicated mid-woofers are over-rated