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I think that looks great. A lot better than your original IMO. In fact, I think you could just use 3/4" without the 1/2" if you wanted. Plywood is very strong when joined together at 90 degree like your corners. I weigh about 220, and a 3" wide 36" long peice of 3/4" cabinet grade plywood easily supports all of my weight with no reinforcement - I can put one end on the ground and push down on it with all of my weight and lift my feet off the ground (and even "bounce" on it without breaking it). I think you are on the right track now.
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