I agree with Darlene. I am a longarmer also and I do not trim quilts unless I am requested to do so.When left untrimmed it is easy to see why there is not a lot of excess backing left. If it is an edge to edge pattern it will always stitch beyond the edge of the top for good coverage. More often than not the back is not perfectly square when I get it from the customer even if it is 108W backing. I measure both top and back twice before loading. If there is more backing than needed I will shift the top over to save a much batting and backing as I can without compromising the quilting. I too am a quilter and understand how expensive fabric is these days. I will return everything usable to the customer if I am asked to trim. You coud mention to your longarmer when you give her the quilt that you would like to use any excess backing for binding. That way she can put it in her notes and be mindful of that when she is ready to quilt it. Give her another try. I'm sure she really wants to make you happy.
Sherry