I'm having some trouble with advanced picking. When I am trying to move between strings etc. my picking hand tends to move laterally from over or just behind the soundhole, where it should be, to get closer and closer to the saddle, which then throws my accuracy off. Is this common, and are there exercises to help avoid? In general I rest my palm on saddle near pins, but it has a mind of its own sometimes.
Besides slowing down and practicing mindfully, perhaps consider your overall posture. The way you're sitting (or your strap height if you're standing) as well as holding the instrument may be making it more difficult for you.
It's obviously difficult to give any specific advice just via text, but making sure that the instrument is secure and stable without any undue tension or contortion on your part is important for many aspects of technique.
One thing you might try is not anchoring the palm. If you anchor the forearm on the edge of the guitar, a few inches from the elbow, and keep the hand floating more like the arm of a turntable, I think that will give you more control and stability.
By adjusting where on the arm you're planting, you can pick closer to the saddle for a brighter tone or closer to the neck for a sweeter tone. It should also be easier to use the palm for palm-muting.
First off, what defines "advanced picking" relative to other picking?
If you are a beginner or intermediate player and you have not spent time developing basic right and left hand skills you are probably hitting a wall with new material.
There is a large body of basic exercises in most method books that are designed to help guitarists get past these types of issues. At the root it sounds like your body is not completely connected to the guitar yet, or that you may have felt that way but started pushing the envelope.
When it comes to developing accuracy I would avoid things like anchoring palm, pinky finger to the top, or other approach. In the end it may fix what's going on now but limit you later when you try something new.
Developing basic skills and accuracy requires isolating the movement or passage that seems to cause the problem and drilling it very slowly until you cannot do it wrong. You also need to eliminate all extemporaneous movement. The good news is that you recognize this movement of your arm so you are aware of it. Now practice that part slowly with a mental focus on keeping your hand where should be and you will come to feel that at normal.