You can bypass the pricing by class by doing the following:
Add items to the cart; enough to be in the next price class break.
Fill out the shipping information.
Calculate the shipping.
Remove 1 line item from the cart
Check out.
Voila! You get reduced pricing, instead of the price re-calculating.
I just had a customer do this to me.
(Addenda - a solution to this would be the following:
Deleting a row automatically calls the "Recalculate Price" routine)