How about gluing the flat piece directly to the scale with silicone caulk, drill a couple of holes in the flat bar to access the scale mounting screws. put a bead of caulk between the top back of the scale and the table/bed.
Silicone has a tenacious bond to non porous surfaces, metal glass etc. People often mistakenly use it on wood, brick etc. and it fails, giving it a dubious reputation.
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