[Rebelwork]

There are always a million ways to skin a cat, but this would be how most would do it. Because the span is 7', you will need support framing under the seat. 2x3s would be fine.

View attachment 444871

This is how it is normally done in cabinet shops. Trim carpenters usually do the same..

 

[Rebelwork]

Any big box store has 2x3s.

X1...lol

 

[Rebelwork]

Why must the top be one solid piece? That's a recipe for an amateur outcome if I ever heard one. Do a neat & tight job with permanent installation of triangle pieces on both sides. You'll have nice big center rectangle to lift with a piano hinge at the back. With the top raised there will be good access to the entire storage area. Work carefully and the space between the center and side sections can be 1/16th inch and look totally professional. Your desired approach, IMO, will fail.

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It's either a three piece with the center on piano hinge or its solid on top with hinged or panel clips on the bottom.

It's not complicated..