I walk every morning in the woods with my dogs in softsole mocs and make an effort to use a forefoot / neutral strike. As others have said, it takes some time to "retrain" but slowly it is moving into my running stride as well. I ran track for years and was always either on my toes or heel striking (when distance training) and I really had a lot to unlearn--but my shin splints are now a thing of the past. Check out Chi Running from the Library if they have it and give it a read. I just got it last week and have found it helpful.
Better to run slowly in correct form and build up--especially if you are still dropping weight. I've lost about 30 pounds so far and that has really helped with running. Or has running helped with that? Another chicken / egg thing. Good job that both are tasty