How can I attach a 1/8" strip of steel to MDF so that it stays secure forever for eternity?
1) Use an 81" length of metal with a 'T' cross section. Cut a slot down the middle of the 81" edge of the panel to accommodate it. Dry fit, then assemble with construction adhesive. If desired, 'pin' the T-bar in place with nails or screws through the surface of the door.

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2) Use an 81" length of metal with a 'U' cross section and 1.5" outside dimension. Use a router to rabbit each of side of the 81" edge so that the U-channel fits onto the edge. If desired, 'pin' the U-channel in place with nails or screws through the surface of the door.

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3) Use an 81" length of metal with a 'U' cross section and 1.5" inside dimension. No routing necessary. If desired, 'pin' the U-channel in place with nails or screws through the surface of the door.