Sorry, I have never tried them. But, I have found the Earth shoe soles pretty stiff. I am not sure I would want my foot held into the negative heel position while running, and I don't find that the Earth shoes flex much. I think they would make it difficult for your foot to transition to the push-off part. (this is not based on experience in the Earth running shoes but I have worn the regular Earth shoes and I run.) My mom had a pair of the athletic Earth shoes and loved them, but she only walked in them. If I were going for non-traditional running shoes, I would go for the Nike Free model or those heavy-duty glove like things for my feet. I am really tempted by the idea of building up stabilizing muscles in my feet.
As far as shin splints go, I used to suffer from them terribly but have had no problems with them in the last few years. I was fitted into a pretty mainstream stability shoe at a running store and mix up my running between pavement and grass. I think the biggest factor though has been a slow, gradual buildup ala couch-to-5K.
Good luck!