I won't be doing it, myself;  that "backside" is much steeper than it looks on the snowy picture. {no way to even get close to culvert area(on backside), backing up with JD4020 and bushog = too dangerous, to be stupid}

I'll hire someone with a CAT 320 excavator or similar.

Another thought

 My tile guys, will be in the field, next door, this Spring and I will ask if their CAT extend-a-reach backhoe might get it done.(maybe , maybe not = not enough reach)

I moved a little dirt, yesterday, farther down the ditch area, and it was frozen about 6-8" underneath in some areas.