Hi Don, Kimberly here from landscape solutions for you. Gophers can do a lot of damage to a landscape area. I am sorry to hear you have had such a problem with them. Being a landscaper, what I would recommend first to do is to contact two to three different pest control companies in your area. Get some ideas from each one and cost. There are safe chemicals that can take care of the gopher problem as well as defering them from your area.
The next step is the erosion problem. Unfortunately it sounds like your bank or hillside is pretty much ruined. It may take starting from scratch. You can apply a weed and root killer down to take care of any remaining roots of the Honeysuckle. Once this is done, I would wait around a week, go ahead and prep the area as much as you can. Jute is a great commercial landscaping fabric for hillsides or banks. It is made of burlap and is also used for erosion problems. Once you apply the Jute, you can plant new Honeysuckle, other ground covers, or even some evergreen shrubs.
An option at this time also is to get in touch with two or three landscapers in your area and get some estimates and ideas from each of them. This may give you some other alternates on what to do with the hillside as well as what plant specimens to plant.
Thank you for asking the question, and if anyone else has some suggestions for Don, feel free to write here in this section. Don, let us know how you made out and the best of luck to you. I hope your problem can be resolved quickly.
Kimberly