This may not offer quite as much shock protection as the display bracket being discussed
here, but I am planning to mount my display using clear mounting tape sandwiched between a polycarbonate window and the OLED screen. The window (1/8" thick, matching the thickness of the wood case wall) will be cut and sanded to size so that it is a press-fit in the opening. The window/display assembly is then (gently) pressed into the opening from the inside of the case.
By placing the tape on the display first and then the window onto the tape, I think I should be able to align the window accurately over the display. The tape will be slightly larger than the opening, temporarily holding the assembly in place on the inside of the case until a foam backer fills the remaining space in the case and holds everything in place.
I'm waiting on my DNA board to arrive but I stuck a piece of tape on my stove clock to test the idea. Very little (if any) optical distortion, and until the tape is really pressed, it is easily removed and repositioned. The tape is ~1mm thick and is somewhat pliable/rubbery (even after sitting in a toolbox for 5+ years) so perhaps it will isolate the OLED a bit from impact.

...and thanks for the encouragement, santo!