MIT vs BSD makes no practical difference. However, the license you have now is not actually MIT, but MIT+your extra restriction. That makes it not open source and a liability for anyone that would use it, since your extra restriction could be interpreted in any number of ways.

One way to keep the option of legal offense against clones is with differently-licensed assets. MIT your code, but choose one of the non-commercial or share-alike Creative Commons licenses. There are lots of them and you're bound to find one that fits your purposes.