I ended up buying the warning triangle from ECS Tuning (
ES#2063860, OEM #71606770487, $29.95). I originally ordered it from getbmwparts.com but they said that they are no longer available. I was able to get the rubber straps from them (OEM #
51-47-8-398-113, $9.79/ea.)
Here's a picture of the warning triangle mounted in my car with one of the straps unhooked to show the nub on the rubber strap and how it hooks into the keyhole slot. The other end has a steel pin through the rubber to hook into the lower slot:
