Is This A Bad Move?

disknic, the problem is not so much how the speaker sounds, it is how the cabinet sounds which is dependent on its construction. 1/4" plywood backs are going to resonate like a drum head and other loose parts are going to vibrate and potentially make a lot of noise. 
The best cabinets for bookshelf speakers have no backs at least in the bookshelf section and are solidly constructed with fixed and dovetailed shelves at least an inch thick. Knock down construction is a nightmare.
If you wind up with a few buzzes you can find them by damping various parts with your hand. Once you find them just jamb a little butyl glazing tape in there and that should stop it. You can get the tape at your local Portland Glass dealer or any place that glazes windows.
The large Advents sound best upright on stands. Why are you putting two pairs of speakers in the cabinet? Doing that will ruin your imaging if you care about that.

Thanks for the suggestion, mijostyn….I'm using the bookshelves because I just picked up the Advents a month ago or so and don't want to ditch the ADS L-810s. I won't play them together, just one pair at a time. The units are handmade, not knockdown, and I won't be playing music at a loud enough volume to excite any buzzes, hopefully. The shelves are secured really well to the cabinet walls with metal hardware, which should help. They were made by Thomasville Furniture here in NC, which is no longer in business (along with many other furniture companies). The room doubles as a den/office, so space is at a premium.

If you can get just one sheet, OC703 one inch thick, cuts with a knife and you can fit beautifully around and behind. This will kill all sound and most vibration. Its a yucky yellow fiberglass but wrap it with the right fabric and it will look pretty darn custom professional. Wouldn't need much and the whole thing would be crazy cheap yet effective.

I'll definitely give the OC703 acoustic paneling a shot.