It sounds your problem is probably due to the change in character of of the hill side. I think Willow probably would help a bit but not enough to fix the problem. Some towns are reluctant to plant Salix/Willow plants because the roots can be very aggressive do a lot of damage to plumbing if it's not getting enough water.
If the bed does continue to stay soggy you might want to plant more bog type or water loving plants to take advantage of this. Not knowing where you live or your zone, I can't really suggest what types of plants would do well there.
