I do not think there is a solution that does not involve altering the cord and assuming that its properties remain intact.
There is no timing mechanism for you to "know" it has been 15 mins. With the two chords problem, you had to use the "other" chord as a method to "time" your chord. No matter how many times you light the chord you can never know how long it has been or how much time is remaining to be burnt. We can say for certain instances, that we can light here or there and get 15mins, but in reality we never truly know how long it has been without an external timing source. edited: (besides 30 mins)