Halved Joint on a glued up board?
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Inspiration
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Mock Up of Design

NYC based amateur woodworker here. Been planning on building an open bookshelf on the wall for my partner. She wants the shelves to be 14" deep (and roughly 9' length) but unfortunately that width makes it very difficult to find finished lumber that doesn't need a jointer or a planer.

I've thought of simply gluing up two 7" boards together but my original plan was to use halved joints to connect the overlapping horizontal and vertical boards. Would that still be possible with a halved joint? I fear I'm just overthinking this whole thing and would love some advice. And would love to ideally keep the width I'm going for.

Also, the boards would be 1.25" thick. Thanks!