It is very important "how" you tell the story. Even the best story will not work if you're presentation is not to the point. Being able to communicate effectively is key for a consultant and that is also what they want to see.
I think you can use the story (if you can't think of anything else). You should tweak it a bit and highlight the key points a bit more.
Key things to remember:
> Structure your story (1) Situation (What is the context) (2) Complication (What was the conflict?) (3) Solution (How did you resolve the conflict?) In your story 2 and 3 is not clear enough.
> Be specific but keep it simple. It is a fine line between being too generic and adding too many unnecessary details. Your mention lots of details in your stories that are not always helpful for proving your point.
> Not longer than 2min. It is important to be to the point and bring across your key messages in 2min or less. So practice your presentation.
Good luck! I am sure if you go over it again and practice, you will have an excellent story to tell :-)