I've recently made a crate for E39 Diff to be shipped here in US and I pretty much used identical materials, literally the same grade plywood and 1" square wood pieces.
I'm curious, which carier arrived with?
I've done some international shipping (Europe to US) and DHL is typicaly the cheapest.

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2010 BMW M6 * Black Saphire Metallic * Full Black Merino Leather
2019 BMW X3 M40i * Alpine White * Mocha Leather