You are actually lucky that the glue did not stick to the belt, because you would have irreversably altered it, reducing its value. Mechanical attachments are always better than adhesives, because they are more reliable and less apt to negatively affect the condition of an item. Even though customers always think they want "invisible" means of mounting, that is often a practical impossibility. What they really want is an
unobtrusive mounting method. Advise them to look at how objects are displayed in museums. The mounts are visible, yet they do not detract from seeing the object because they have been made as unobtrusive as possible. Stitching through the lines of existing stitches with matching colored thread, as James suggested, might be a good alternative, but you will probably need some other way of supporting the heavy central element.
Rick