the only way i know to fix this is to skin the quilt.
i'm shocked that a professional LAer gave the quilt to you in this condition and had the nerve to charge you for this workmanship.
you need to return the quilt to the LAer and have them load the quilt back onto the frame so that the quilt can be skinned quickly and safely. you can look up "skinning a quilt" on youtube so you can see the method.
i would also get a refund of all monies paid and then give it to someone else to quilt for you.