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On Edit:
Ok hears the scoop. I wrote I couldn't figure out what you were doing from the pictures, but I thought Molly Bolts could be an answer. Well when I posted it, it occurred to me what was going on. Molly Bolts would never work.
Here is my second shot at this. Thinking you might not have the clearance for it, but maybe with the right hammer and construction glue it might work.
Since the plywood edge is a FUBAR, you'll need to replace it with something structural. My thought would be maybe something like this. Pound and glued into place, then drilled and screwed.
Clicky
