If you're going to do it yourself you can get a nice set of files that will work well by going to your local Home Depot and buying a set of the files that they use to clean the tips of oxy-acetylene welding torches. They're cheap! (Last I checked they were under $5, but that was a bit ago).
Also, it's very hard to tell from the pic, but it looks like the back of the slot (the part closest to the tuners) sort of "vees out" whereas the other strings seem to be sitting deeper. If you can deepen the slot in the back, and make sure that your string is wrapped around the peg with the string spiralling down from the hole in the peg (so that you have a steeper angle over the nut) you ought to be able to make it stick better without changing the action.
Man, that's harder to describe than I thought it would be. If it doesn't make any sense, holla! I'll try to answer specific questions.