Teams are wrapping the transparent plastic bag multiple times around the egg to create a cushion and/or obscuring the rounded part and/or tip of the egg. Are there any regulations around this?

Yes, per rule 4.d.iii(4) the ES may require the competitors to place the egg in a "thin" plastic bag, however to be considered "thin" the leading and back tips of egg and must only have one layer of the bag covering it to avoid cushioning the egg from potential impacts.