Allergies in my house. Would there be an ingredient that would replace the cream (coconut milk, soy milk, magic?) and still use this technique?

You might be able to use coconut milk and perhaps a bit of coconut oil. I don't think it would separate quite the same way, and it might give you coconut flavored eggs though. You might also be able to use silken tofu along with whatever neutral fat you prefer. Soy milk and products will caramelize, and the soy milk in those aseptic packs often is slightly sweet because the processing causes a slight caramelization. The only thing I can't say is if it would thicken as the liquid evaporated.