@NoriaCorp. The solution is simple. Take advantage of the Custom Carrier Shipping API built in to Shopify. It allows you to present rates to your customers that you control. If you are losing money on shipping with existing Shopify shipping setup, you are free as a bird to setup your own connections to FedEx, UPS, etc, get rates, and present them.
All merchants are free to go with a number of options these days, including speciality Apps for shipping, the custom approach, and status quo.
Note this in HunkyBill's footer: "Specializing in Custom Shopify Apps."
Sounds like you are asking for a "canned" solution while HunkyBill cooks up each one fresh with the best ingredients as requested by the customer. Hopefully Shopify will make generic support for the dim pricing soon but even when that day comes it will not be perfect. No cart/platform can claim perfection. You know what the apps cost on an ongoing basis and you know the status quo. If you want custom, flesh out your requirements and ask for a quote, from HunkyBill or others.
I'm not looking for custom - I want native support for dims, but as Shopify is obviously slow to implement, third-party solutions are the only option at this point. It didn't escape me that HunkyBill is (somewhat) subtly marketing his wares by hinting that there are solutions out there which can be had "simply" and "easily" - for those with the coding chops, of course. Boxify looks promising, but it's frustrating to consider paying for something that should be built in, especially if Shopify is as close as Bill claims they are.
Shopify's single package weight based calculation of rates is effective when it comes to light, intermediate or little heavy orders. However, when heavier orders come up which need to be packed in separate boxes, then calculation of rates can be handled via apps. You can try the Multi carrier shipping label app which allows you to provide a threshold weight beyond which a new box is selected. For example, if you have items worth 25 lbs in your order and you have defined 20lbs as the threshold value for single box, then the package will be packed in 2 boxes and shipping cost will be calculated accordingly. There are other ways of packaging that can be tried using the app like defining the quantity of items that can go inside box.