Shopify is NOT Always Calculating Correct Shipping Costs

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I sell widgets via Shopify with the Shopify Plus plan. Approximately 70% of the orders on my site are for a single widget. The widgets I sell are fairly large (12"x9"x8") in size. Therefore I have set the default shipping box to this size. The weight of each widget is about 5lbs.

When a customer is in the checkout process, the shipping cost they are quoted is based on the weight of the quantity of products being shipped within the default shipping box size I've set as my default (in this case, 12"x9"x8").

However, 30% of my orders consist of more than one widget. In some cases, 6 widgets are ordered at a time, sometimes more. It is impossible to fit more than 1 widget inside the default shipping box size. If I were to ship 6 widgets, the shipping box size required is MUCH larger than my default size (24"x18"x12") and the total weight would be around 30lbs.

Here's the problem I'm running into:
The shipping quote offered to any customer ordering more than one widget is going to be under-quoted because if a customer orders 6 widgets, they are only paying for the shipping of 30lbs of widgets stuffed inside a 12"x9"x8" box, which is impossible for me to do given the size of my widgets. Since Shopify only calculates the shipping cost based on the default shipping box size and does not factor in the dimensions of ANY product, the customer pays for the shipping of this small box, but I end up having to pay for shipping label of a 24"x18"x12" box (the smallest box that 6 widgets can fit inside of).

As a result, I'm losing a significant amount of money on shipping for about 30% of my orders.

I don't want to overcharge 70% of my customers to compensate for the losses I sustain with the 30% of orders.

My question to this community is: What is the best non-workaround solution to this you've found that does not involve a 3rd party app? And is it possible that thousands of other Shopify sites are experiencing the same issue?

Thank you!

P.S. Shopify Partners, please do not respond promoting your 3rd party app. I'm aware there are shipping apps available. This message is intended for other shop owners and Shopify Product/Program Managers & Developers.

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Out of curiosity, if you are losing this much money by charging incorrectly for shipping, why not use a third-party app that would solve the problem and save you money? Is it the principle that Shopify should have more than one box size? 

Realistically, your best bet without an app would be to create 2 products of the same type. One is for 1 widget and the other is for 2 or more. Create two shipping profiles, with your single item profile calculated via live rates, and the second profile having a weight-based rate that is tiered. Let's say that for each additional widget, your shipping cost increases an average of $6 and your widget weight is 5 lbs. Your first tiered would be $6 for 5 lbs, second would be $12 for 10 lbs or more, and so on. 

This still won't be perfect, but it's as close as you'll be able to get without using an app. 

Co-Founder / CEO @ Intuitive Shipping
Execute a strategic approach to shipping | Intuitive Shipping | Smart Boxing | Automate Shipping Profiles
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Amen to the P.S. section! I'm so tired of the 3rd party app suggestions. I'm already paying a decent monthly fee FOR Shopify, why should I have to pay even more for an additional app just to stop losing money on shipping because Shopify's algorithms can't correctly determine which size box to use like they claim it's supposed to? You're definitely not the only one experiencing this issue!! I've been through so many of these Q&A forums, and haven't found anything substantial yet. Incredibly frustrating