Bearing in mind that the overall size is just 340mm sq I would wanting a totally invisible means of support. My thought would be to simply drill the wall, plug and screw at the mid point (top) of the two inner uprights (roughly 110 ctrs). Then, with the screws in the wall file the sides and bottom off to create a sharp spike on the top from the countersink head. Alternatively modify the screws first and screw them in using pliers. Next drill the uprights to sit over the screws. The sharp profile of the screw head should be sufficient to grip the oak and keep it snug to the wall.