Oh Lowena, I sympathise. At my 21st birthday party, arranged by friends, one of them said that I was soooo single-minded and I spent the next 40 years thinking that it was a compliment.
Anyway, boxes are a good idea. I have a stack of those with clip-on lids but they fit into a sort of chest so that you can pull one out completely and not upset the stack. I got it in a hobbycraft, don't know if they still have them. If you have a table, one would probably fit underneath.
You will suffer relentless chivying if you try to opt out of the mystery quilt.