I found this with a board search. In the following text Bob Novy is replying to someone whose E string was not sitting in the slot properly.
Oh, and it just occurred to me; you did say that you were using thicker gauge strings now. It might be that the new larger D string is too big to sit in the slot properly, in which case the slot will need to be filed a little.
Here's what Bob had to say.
be careful. I would recommend using a needle file (or better yet a nut slot file, but not many of us have those). Ideally, you'd like a half-circle groove that precisely fits the string. However, you don't want to cut it too deep because then the action won't be consistent with the other strings. You also want to have a well-defined witness point, i.e. you do not want to have a rounded, curved entry on the neck side of the saddle, and the back side of the slot has to be deep enough so that the string is fully seated on the front (neck) side.
If you're patient, have good eyes (or a magnifier), and understand the concepts, it's not too hard - otherwise, have someone do it for you.