refreezing ice cream

Upon researching techniques for refreezing ice cream, I discovered that the air created by agitating the ice cream before the initial freezing is lost in the melting process. This causes ice crystals to form in the ice cream which considerably changes the consistency. In my experience, the chocolate chip ice cream I used formed noticeable layers of ingredients. It may or may not be "safe" to eat refrozen ice cream (depending on the temperature of the melted dairy) but I'm not intending to eat the artwork anyway.