Just a thought, but oil can eventually damage neoprene foam, turning it into sticky gum, which may be a long term concern.
When I was looking to reline an old English gun case, I was looking for wool baize material, and my wife mentioned that if I wanted thicker wool, to look for all wool Melton coating material in the local fabric store. She was right! Lovely weight for gun pads or case lining, lots of colour selection (dark greens, browns, burgundys etc) very classy material, and usually runs $20-40 a yard.