On the product pages- instead of adding to cart and checking out the standard methods with a gateway— the product page would have a button / lable to “request a custom price quote”– then still use woocommerce customer info, shipping address, etc— and email that info– or add to an “Custom Price / Quotes” menu and list them similar to receiving an order. After the price / shipping is calculated, the customer is notified, and can agree to the price, and it would then be converted into an order and processed through woocommerce.
It could also be implemented in a more simple method, with the goal of making an easy way to convert a price quote to an actual order transaction.