I found my first Woods Hibernia this past winter and it is much worst than yours and nothing can repair the damage already done, and I did use peroxide on mine and gingerly tried removing all the excess dirt I could but the coin was pretty far gone as far as original surface being eaten away.
There is a saying "A coin is what a coin is" all the cleaning in the world, whether by you, NCS or anybody else cannot make a coin uncorroded again.
Do the best you can with removing the dirt, since dirt traps moisture and other contaminants that will continue to corrode the coin.
Peroxide is fast, than give it baths in warm distilled water for up to 24 hours, dry thoroughly and then protect with either R wax or Blue Ribbon.
Don