I need Shopify to select MOST EXPENSIVE shipping rate at checkout (not cheapest)

[KatesShop]

I have set up my shipping rates to calculate based on cart value as this usually pretty accurately reflects shipping costs of the item/s.

I have some products that incur additional shipping costs based on either size, weight, fragility etc.  This is NOT just based on weight alone.

I can set up different shipping profiles and rates for these products, no problem.

The problem comes when people order a 'normal' product in addition to a 'bulky' item.

Shopify either combines the shipping rates (adds them together) and charges an absolute fortune that will put most customers off (!) OR it selects the CHEAPEST of the rates and this isn't enough when you're sending unsually sized/shaped/fragile items!

Is there any way to tell Shopify to select the MOST EXPENSIVE of the rates?

It seems absolutely crazy to me that only the cheapest is calculated. Why would you want to give customers the cheapest of the rates and lose out?? I can't run my business that way.