Chaz perhaps instead of paying for a quote engine you could just link to a pdf with the rates for your favorite carrier. You could either create it yourself or just remove their logo so they'll have to call you to find out which carrier it is. Even when your go to carrier has different rates for the various zips at the most you probably have to link to is three pdfs.
I was once told by a carrier that posting their rates in a flyer or on a website requires their approval as well.