Is the actual problem to solve that: vampires aren't immune to petrification, or is the actual problem to solve that: an essential item can be lost in an unexpected way? It seems pretty self evident the actual problem to solve is the later.
I think vampires should remain subject to petrification. Some vampire storytelling outside D&D even has some failure modes ending in petrification. There doesn't seem to be anything that reasonably says they should not remain subject to petrification.
As such, I think making vampires immune to petrification is not a good choice to solve the actual problem to solve, and a solution more directly addressing the actual problem to solve should be found. I'm sorry; I'm just returning to this game after 20 years so I don't know what that is, but other people here have commented on that and I bet people can come up with a great solution.
Maybe there's a way that on that vampires "death", the cloak can be created on the floor? It's been 20 years since I knew all this.