Look around your area for carpet binding services. There are two main methods (a) using a heavy duty serger sewing machine to create stitching over the edges and (b) wrapping a tape product over the edge and using glue or stitches to keep it on. Most carpet shops would know where to find a binding service - not all processes may be robust enough for marine use. Boat trimmers/canvas workers may have the facilties to do the work or they know where to send the work. It's not expensive in relation to the cost of carpet.
Serging
Binding