How to get the most accurate shipping calculation

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I am opening store selling fabric by the yard. This will be pre-ordered so I will not have it in my hands to calculate shipping. I'm trying to figure out the best way to have Shopify calculate the shipping for my customers. I am willing to take a slight loss rather than deal with refunding my customers for a shipping overage, but I'd rather it be as accurate as possible from the beginning. Here is the best breakdown of my products and the estimated shipping methods:

 

PFRE (padded flat rate envelope) will hold 1-3yds average - more or less if thinner/thicker fabric
0.45 lb – 2.5 lb
$7.75
 
MFRB (medium flat rate box) will hold 4-8yds average - more or less if thinner/thicker fabric
2.5 lb – 7.31 lb
$14.75
 
LFRB (large flat rate box) will hold 9-14yds average - more or less if thinner/thicker fabric
7.31 lb – 11.38 lb
$20.00
 
So if a customer orders 3 yds of an average thickness fabric, it will fit in a PFRE, however 3 yds of a thicker fabric would not, or I could fit more of a thinner fabric and not need a MFRB for 4yds of fabric.
 
Does anyone have insight on how to best handle this?
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