This is what happens when show organizers don't think about the restrictions they're imposing. A great many designers sell their copyright to the magazine when they have a design published. So, yes, they are the designer, but they no longer hold the copyright. Where does that leave someone who wants to show that quilt? Maine Quilts specifically states you need written permission from the designer...period.
If I were you, I'd track down a phone number for McCall's customer service, talk to a living human being and explain that you need written permission from Debbie Beaves to enter and publically display a quilt made from her design, regardless of who holds the copyright or what the policy of McCall's magazine may be. They may or may not choose to put you in touch with Ms Beaves.
Other options would be to track her down in Vancouver somehow, and/or contact the Maine Quilts quilt registrar, Susan Bulay (hyperlink is on the entry FAQ page at Maine Quilts website). The entry deadline, btw, is a May 15 postmark, so you have a bit of extra time. Wishing you the best of luck.