Around here, there are a couple fireplace shops that have a bigger selection of door rope than the home centers or hardware stores. If you don't have a stove dealer near you might try that.
There must be more than one variety of gray rope, because the last time I bought gray it was the stretchiest/squishiest I'd seen. I remember I really compressed it when installing, and it still was too easy to shut and latch the door. I replaced it after one season.