Peonny, the rain is really heavy! I am afraid the drainage is not good enough for any peony. i wold be terrified if I see my peony in a puddle. Other forum members can add their experience but I wold never allow (if I could) a peony in such high water. If you have a lot of rain like this it could be a good strategy to plant them like Carol Adelman does - on the ground level and make a hill over the plant:
https://www.youtube.com/watch?...
Regarding the depth I wold add more soil, Itoh roots can be planted up to 4" deep. What zone are you in? The colder climate the deeper one would plant peonies. Good luck!