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Do us a favor and ask the guys who redid your kitchen what that material is. HDPE is $240ish for a 4 x 8 sheet. You may have stumbled onto something that slides like HDPE but doesn't cost as much.
To solve the problem of not getting grip, you could buy either some steel tubing or 90 degree angled steel and recess it on the edge. Then you would have a box that would be as good as any box you would find in a park.