A single product that ships in multiple boxes

I am not sure about your situation, but maybe some kind of work-arounds can be applied to that.

I mean, not creating that partially-shipped product as 1 simple product,
but maybe some kind of product variations or bundles or combo, etc.

As far as I know, in the descriptions of those kind of bundle/combo extensions, there are some settings for shipment.

For example:
Product Bundles
https://www.woothemes.com/products/product-bundles/
https://docs.woothemes.com/document/bundles/
———-
Select a shipping scheme: are the bundled items shipped together, individually, or not at all?
———-
Bundled vs. Non-Bundled Shipping
If your bundle consists of items that are meant to be assembled or packaged together, then leave the “Non-Bundled Shipping” box un-checked and go on to define the physical properties and/or shipping class of the product bundle, as you would do with any other product.

If, however, the bundled items are shipped individually, their shipping properties must be retained, since each item will contribute to the final shipping cost as if it was added to the cart alone. In this case, the checkbox must be ticked.
———-

Maybe this will be helpful for your situation, or at least give you a hint for a start…

I took another glance at Product Bundles and it seems like the best option for what he is selling.

In the meantime I suggested to WooCommerce the idea of allowing a single product to have multiple shipping containers. For clients that sell large products (furniture in my client’s case), this becomes quite common to have to ship multiple boxes.