I wouldn't mount it backwards like that. Mine is "mirrored" they're meant to mount on the drivers side to not block the license plate. I would mount it as pictured because of how it attaches to the sheet metal. Closer to the hinges the better.
My handle is accessible, I wouldn't call it "wide open" but its easy enough
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Search for "underbody tool box" available in many sizes, steel/aluminum from ebay, Northern Tool, Tractor supply Co, etc.
https://www.ebay.com/i/201578100897?chn=ps&var=500787114997
https://www.northerntool.com/shop/t...e+truck-tool-boxes+underbody-truck-tool-boxes
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