Does your existing chemise have a buttoned gusset? If so, you can unbutton it and get a wide-necked one immediately. Saved me a lot of frustration with Peeking Chemises.

ETA: Oh! Also, if your chemise is a comfortably long (say knee-length), you can also skip the under-hoop petticoat. I understand it seems to be optional in period anyway, and between chemise and drawers you'll still be nicely covered. Hope to make a simple project simpler!