How to ship this item to AK

Sold a toy which is in an open box. By open, I mean the manufacturer doesn’t completely enclose the box so this animated toy can perform (move, speak, sing).

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The box itself is about 15x14x8 and with the 2.1 pound weight would cost $16.45 Priority Mail to the PO Box in AK, but if it goes up to just 15x15x9, the price increases to over $50. In other words, that small increase would make it cheaper to send 3 as-is than one in a slightly larger box.

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Sending by USPS Retail Ground at the post office (this is not even an option for an online-printed label) wouldn’t be much better, about $49.

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If it goes a bit larger, it jumps to over $71.

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Is there any practical way to send it for around the $16 price?