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If the board is truly 7.5" thick/tall I'd suggest looking into special brackets like??.?

Otherwise, a clever method if the situation makes sense is to cut? the back of the board a good 1-1.5" from the back edge, and use it to mount directly to the wall with recessed anchors. Then use dominoes in an array to push the rest of the board against the mounting slice, and the piece will be impossible for the next guy to figure out how you did it once the adhesive sets and the dominoes swell. If you dry fit the dominoes beforehand like you are supposed to, you can tweak the joint line to make invisible, which shouldn't be too tough on ash given grain orientation. Fun project!