I use Target plastic placemats (approximately 12.5" x 16"). They're the exact same width as a Cricut mat, but I don't know what the Silhouette mat size is. I covered it with Contact shelf liner, and made a pattern in the software for concentric rectangles, starting at the maximum cutting size and going down by the 1/2". Cut the pattern out, then peel away the outer piece, run along the edges with a sharpie to make the "placement" grid, from the outside in, which is more accurate than a pre-printed one anyway since it's where your cutter will cut. Mask the edges and spray with Krylon repositionable spray.
Target clearanced the placemats in my area though, don't know yet if they're just putting new patterns out or completely discontinued. Last year the 4th of July placemats were the same size, but too thick. I don't know how well it would work taping 2 together.
If you have a plastics fabrication company in your area they may have some kind of material that's the right thickness that they can cut for you, but often these companies massively upcharge for people coming in with tiny jobs like that. If you're lucky they may just give you scraps.