Ok then, well how about you fold them down and stack one or more on top of the paper mountain & allow the quilt to drape onto there. If they have the removable legs, take them off & stack only the tops on the table. You could even fold another quilt to lay under the tops of the trays... anything to create height for the drape to rest on. That's all...
Where there is a will, there is a way. You're an artist, right? Be creative. And if all else fails, fake it until you make it!!