How do I disable Commerce cart order refresh to preserve custom prices on line items?
You're approaching the problem incorrectly here. You shouldn't be trying to disable the cart order refresh. That includes things like discounts, taxes, etc. that may actually need to be applied to line items on the order in the future.

Instead, you should find a strategy to enrich the line item with the information it needs to reset the price to the proper custom price during the pricing process. This is the approach utilized in our old donation examples where customers can enter custom prices to donate:

https://drupalcommerce.org/videos/tutorials/donations-custom-line-item-types

I have no experience with the module you're using, so I can't say how to keep working within the framework it provides. Generally speaking, though, you could make this work by adding a price field to the line item called "Custom price" or something and then creating a pricing rule that sets the unit price of line items to the custom price at the appropriate point in time.

Alternately, you could store the necessary information in the data array of the line item, but then you'd still need a product pricing rule with a custom action that knows how to inspect the data array and reset the unit price to the appropriate amount.