Q about raised panel construction on sub enclosure

When I redecorated our livingroom, I installed raised panel wainscoting and one raised panel wall. The panels float. It's all painted MDF. Styles and rails are 3/4, panels are 5/8.

I'm looking at building a sub enclosure. I'd like to clad it with raised panels and paint to match the room. I'm worried about vibrations and rattles.

The sub will probably be an 18" Dayton Ultimax but that is not set in stone.

Obviously, the panels cannot float. I will glue them in. Any thoughts on filling the spaces, perhaps with construction adhesive or similar?