Nice! I'm guessing your FIL appropriated the apron, but maybe not.
I can't point you towards photos, but some have run wiring through dado between the open baffle parts. As I recall, the cleanest used a channel around driver hole and a centered slot. Could also run up side and an intersect driver opening. Both may be possible still if you haven't glued back piece on.
Fussy to wire that way, but a really clean look.
You could also run wire externally in flex loom and some clamps to keep it crisp and clean.
I'm not a fan the look of stained Baltic Birch and if I wanted color it a bit, would use dye tone coats using between clear coats. This assumes spray capability. To my eye, most stains tend to obscure the muted grain of birch and look blotchy. It's a lot like maple in that regard. Gel stain mitigates that to some extent.