I have found that if you visit a gasket-making company 'in person' you can score some scraps of rubber for free, but make sure you throw some beer money at the guy that helped you.
They have all thicknesses of hard and soft rubber materials including cork in the form of 'garbage' that comes off the dies. They keep and recycle it.
If you go with the weather strip, try to find a quality thin 'closed cell' type of neoprene to minimize compression and bleeding of the seal. A trailer or professional truck supply is the best bet-not a home store.