Please note by "side" I am not referring to anything that extends forward of the baffle and could cause a reflection.
You don't understand. The problem is reflections At the frequencies we are talking about your speakers are spherical radiators.
So anything with a wave length longer than the width of your baffle will not be reinforced on a stand, but will be in your arrangement. The really "chesty area is 100 to 180 Hz or so. A 100 Hz tone has a frequency of 11" and 180 Hz 6".
Now away from boundaries the speaker is a half radiator (hemispheric), at a frequency above where baffle step loss starts to occur and a full space (spherical) below that.
For a small bookshelf with a baffle width of 6" the speaker is 3db down at 760 Hz and falls off 6 db per octave below that.
A larger one with a 9" baffle is 3 db down at 507 Hz.
Now these losses are compensated for in the crossover, or should be.
Now in your arrangement the speaker will be radiating in half space at all frequencies and if BSC compensated will have a rising response.
The next issue is your box you intend to construct. This will have a volume, and therefore resonance, and will also have parallel wall reflections.
I just don't understand why you want to put a speaker that is already a box with a grill, inside another box, with a grill.
If you have to put a speaker on a shelf of an entertainment, center, which is what I think you want to construct, then put the speaker on a shelf protruding slightly from the shelf and keep the shelf as full of books as you can. You want to absolutely minimize the dead space that leads to terrible ills.
You may not like the answer, but that is the physics of it.
This may help you further.