How to manage multiple shipping box sizes for weight-based rates?

Try reaching out to the guys at Advanced Shipping Manager. https://apps.shopify.com/advanced-shipping-manager That app lets you set unique product sizes and multiple packages for for items. As well as a ton of other granular shipping settings. They been super responsive to us for customizations, and as long as your preferred carriers have APIs for getting rates they can probably hook up to them for you. Worth a shot at least.