It looks like the TD12M could fit in the Eminence 4012HO hole, depending on what you might need/be willing to do.
Blow-by-blow on dimensions; TD12M's dimensions in in., followed by 4012HO's in ():
Overall dia. 12.38 (12.5)
So that works if you don't mind a .06" annular gap around the TD12, or you could fill it.
Baffle hole dia.: 11.06 (11.18)
If enlarging the baffle cutout is necessary, the way I've done that is to put a roundover on the top edge, then use a pattern bit with a top bearing running on the enlarged part.
If you don’t have one I’ll send you one.
Mtg holes: .28 dia. on 11.59 dia. bolt circle (.25 dia. on 11.69 dia. bolt circle)
Might work as is; if not you could rotate the TD12M and drill new ones.
Mounting flange thickness: .65 (?)
The 4012HO flange looks like it might be a bit thicker; if you think it matters you could use washers with the screws to raise the TD12M and rope caulk to fill the gap or make a spacer
Mounting depth: 6.56 depth (5.32)
From the pic's I've seen of Erich's boxes the depth won't be an issue.