if you line the hole's edges from the inside and behind with a thin veneer that overhangs into the hole, this will give a back plate something to rest on and then can sit flush.

put rare earth magnets into the edges and back plate and it will stay, sit flush and have no screws etc. Be careful and reuse the bit you cut out and it could look pretty slick

the only issue will be if the back is really thin and flexes with a hole cut out. but i think if you do it the way i suggested, the glued on edges should give it stability