Submitting Fabric/Yarn Craft Items to be Judged
I have no experience with this medium, but I would use the packaging problem/opportunity to present your work in the highest possible style.  Instead of sandwiching it between cake boards, consider using a sheet of acrylic for the top bread and thin wood, stained to a shade which compliments your yarn as the bottom bread.

If you have a makerspace ( or library with a laser cutter) near you, you can buy the acrylic sheet and plywood from a hardware store (or amazon) and then cut it to the shape and size you need.  You could also drill small holes in the corners of each "slice of bread" and fasten it all together with yarn, using bow knots which can be easily untied by the judges for closer inspection of your work.