In looking at that back panel, the cap screws appear to be something that was touched on before.
If we think about it, the caps probably cover a stud or screw in the wood. Effectively, it is either a stud screwed into the wood or the head of the screw is covered by the veneer on the other side of the wood. You'd probably have to unscrew the cap screws and see if you could lift/bend/pry part of the back panel (metal or plastic) to clear the stud/screw. **I see screws on the top, and cap nuts on the bottom, suggesting the screws come out leaving a way to slide that panel out, while the bottom stud is a placement / locating stud held down then with the cap screws.
Failing that, try to counter twist the stud out of the wood, or feel on the back side of the panel for a faint depression that would suggest a bolt head there. You could also (destructively) drill into the back side to release uncover the screw or bolt head.
Another possibility is to unscrew both terminals, noting with maybe a little red paint which is the + terminal (if that is marked). I suspect there may be some sealant there as well.
If you now undo all the cap screws, perhaps the panel comes out in two long halves via a center seam. I wouldn't be surprised again if there was glue or sealant on the center seam so that once assembled, not meant to be disassembled. That would make sense from an assembly point of view unless the caps are actually cap screws, then the whole assembly should be free to come out unless sealed with silicone or similar adhesive. its a glued system that resists disassembly, that makes it a bit more challenging.
I would agree that exploring the bottom edges of the grille, or having to cut one side would then potentially free the grille. Its possible the only edge is hidden inside the box.
If one was to decide how to actually built this speaker, I'll bet that it was done in one half with the large bottom (speaker laid flat) and baffle dowel glued together. The drivers installed, then the grille installed and secured. The back panel could then be wired in, any stuffing then put in, then the top panel glued in and the cap screws/nuts and terminals for the finishing touches.
Who knows, you may have to take the terminals off and find someone who has a small endoscope (thin tube with light source and camera on it, maneuverable too) to see inside if you can't get it apart.