Hey - if we are gonna go for it, let's go for it! A 3" layer of closed cell foam, bonded to the hull with 5200, and *then* encapsulated with a rubber skin. Object hits hull, pokes through hull, pushes foam out, lessening impact, rubber keeps any water which comes in contained, and rebounds, pushing foam back towards impact point. Unsinkable boat!

LOL, In all seriousness, I did think about using a rubber mat like you proposed. Perhaps thick enough, it might work. Here's a question which begs asking at this point - What do they put in the tanks of oil tankers? Or in airplanes, to make their tanks self-sealing? I don't know. I bet it costs a gazillion dollars, and only billy gates or a similar largish corporation can afford it.