Setting shipping option order

We sell 4 books in bulk. Each is a different weight and orders can vary from one book to over 1,000 books. Smaller book orders are shipped by Priority Mail exclusively with shipping rates for each book configured in the Woocommerce Table Rate Shipping plugin (i.e., 1-3 English books are shipped in a padded flat rate Priority Mail envelope, 4-18 in a small flat rate box, and so on). Each book is assigned two Priority Mail shipping charges for smaller orders depending on the quantity. Shipping rates for orders that exceed the largest number of books we ship by Priority Mail are shipped via FedEx exclusively with rates calculated using the Ignitewoo FedEx Shipping Pro plugin. When the customer orders a quantity of books that we want to ship Priority Mail, the shipping cost drop down menu on the cart page shows both the Priority Mail cost and the various FedEx costs. The FedEx ground shipping is cheaper than Priority Mail for these smaller orders so the shipping drop down menu defaults to the cheapest (FedEx) cost and not Priority Mail. Is there any way to select the default shipping method that will show up in the drop down regardless of the cost for different size orders or, better yet, have the drop down only display the Priority Mail (table rate) shipping costs for the smaller orders and only show the FedEx charges for the larger orders? Site is The Family Way Publications.