Here's my 2 cents on this carpet issue and in my younger days, I worked for a carpet store and installed carpet. The black rubber is a high density rubber and I think its used to prevent the carpet from moving and slipping around (I see no other benefit from using a rubber back). If you want to repair it, that rubber shelving material looks like a good idea. I would use latex carpet adhesive to glue it. I'm not talking about adhesive used to glue carpet to the floor, this stuff is a white, creamy liquid sold in quart bottles. You may have to look for a carpet supply house to find it. This is what is used to bond the carpet face to the carpet backing in the factory. I have used this stuff to seam carpet together, so I know its strong. If I were to replace my boat carpet, I would get a good quality commercial grade loop nylon with a synthetic jute backing. All carpet today is 100% synthetic material and will not rot or mildew. Nylon is by far the strongest fabric you can buy. My friend bought this exact type of carpet for his 1988 baja and I glued it down to the plywood floor 3 years ago and it still looks great (its the only part of the boat that does look good). The woven backed carpet will tend to slide more than the rubber back stuff, but if its snapped in good, there should be no problems. If you bring your old carpet to a good carpet store, they can cut the pieces using the old carpet as a pattern and bind the edges, then you will only have to install the snaps. This is what I will be doing when my carpet wears out,except I will cut and bind it myself since I still have my old carpet tools.