Aqua-jogging can be a great alternative to running if you are hurt. Yes it's still in the pool but it utilizes many of the same muscles and movements. This article here: http://www.theglobeandmail.com/life/health/alex-hutchinson/the-future-of-fitness-may-be-in-the-pool/article1930179/
discusses some of the differences between running and aqua-jogging. It also has a good workout that I (and Olympic Athletes as pointed out in the article) have used in the past to stay in shape when you are hurt.
It's hard to say how the elliptical will impact your recovery. I tend to play it say and stay ff of stress fractures for a good 8 weeks to ensure I am healthy. Rushing back 2-4 weeks early buys you nothing if you have to go into another 10-12 week waiting period as you heal again.