If you are recessing the sub then add enough extra diameter to the outside rim to compensate for the carpet wrap thickness.
I agree with the parties above. Don't try to bond dissimilar materials. I am completely comfortable bonding ABS or low density HDPE (but not higher density Starboard HDPE) to themselves. One adhesive will not be effective for both.
But I like the overlay idea on the completed enclosure mentioned above.

David