I so agree that mold can have disasterous effects on your health. It is awful. Is that mold on your floor in the last picture or your table top? I would finish quilting that quilt as fast as possible and then call the dry cleaners to see what they could advise for mold. I would be scared to death to take it off the frame and wash it for fear of it falling apart but that's just me. I certainly would use a mask while finishing the quilting or try methods to remove the mold while on the frame.
Wish I had a good solution to offer you, I am so sorry this happened and hope you can resolve the problem immediately.