I have a similar-ish product. For non-discrete items sold at a single price per unit, and where people buy a wide range of volumes, baking the shipping costs into the product leads to strange prices outside whatever sweet spot you choose, because shipping prices don't scale linearly with your product.

The flat rate shipping under $45 in this example is probably because it costs nearly the same to ship half a yard or five yards; shipping 20 will cost a good deal more, but not be anything like 20 times the cost of shipping one yard. So there's no way to bake in a price that doesn't end up generating absurd results either for you, your customer, or both.

Can't you just give a lower price at 10 yards and again at 50 yards for example? Then you solve your baked in price issue and get to offer discounts on high amounts, incentivizing buying more.

Depends on your range of purchase sizes and industry expectations. My product will sell regularly in quantities from 1 to 10,000, and my shipping costs on those vary from about $5 to $50, so I'd have to have a lot of price tiers. That's kind of absurdly broad, though. I'd think fabric and other categories should have a few orders of magnitude less, but I might be surprised.

But, you can do that if it doesn't fly too much in the face of customer expectation. In some industries, like printing, it's common. In fabric I think there's a strong expectation of a single price per length unit, though I suppose you could challenge it.

I don't think lots of price tiers is a good customer experience, so I decided against it as a long-term customer satisfaction strategy. I do wonder if it's costing me sales. Maybe I should set up an alternate brand that does tiered pricing and free shipping.

There's a study of pricing psychology to separate the base and shipping.

[source] https://www.nickkolenda.com/psychological-pricing-strategies...

This is good advice. We do free shipping once your order is over $x. Interestingly when we email offers that are above x and will attract free-shipping the response is significantly better.