It's important to think about what RMS actually means.
There's a good reply about that here, even if not in the context of hilly terrain:
Applying this to your question, it should become obvious that a low RMS is not something you should strive for in this case, as it is almost meaningless. A hilly terrain is basically a map that is locally distorted and "smudged", as geodistance varies with elevation, and is also affected by the angle the photo was taken from. To reference this to a "flat" map, you will need to warp and distort the photo to make it closely fit the map, and that will always be messy.
As Mike Liu suggested, using a DTM to correct for all these terrain influences is the best and easiest solution. But finding such a DTM in sufficient quality is not always easy or possible at all. If this is true for you, you can still georeference the photo, but do so smartly. Think about what actually happens in these transformations: You specify a number of points that are "100% matches" on the photo and the map. If you use a polynomial transformation, the algorithm attempts to find a polynomial curve that makes everything between these "truth points" fit as best as possible. This means: The farther from a CP, the more "distortion" is applied.
There's no inherent benefit of using a lot of control points in a "grid pattern", unless you can place these with a high degree of accuracy. If you are even slightly unsure of identifying control points (CPs), it's better to not use them at all, as they'll ruin the polynomial fitting algorithm. For hilly terrain, I'd recommend trying to find obvious CPs at or around clear elevation changes (e.g. mountaintop/ridgeline, creeks/rivers and the edges of forested hillsides next to farmland, for example. Using a higher order polynomial transformation you'll allow for the necessary distortion to occur to warp the photo to a true flat map. With high resolution imagery such as yours, this should be fairly easy to do.
As this warping is necessary, it actually is a good sign to have a high RMS, because having a match without distortion would definitely be completely wrong. Of course, with higher order polynomial transformations, you risk a lot of faulty warping far from control points (and especially towards the edges of your photo), but there will always be a price to pay (aside the obvious huge amount of processing required).
As to your idea of using smaller areas: If you only need a small area for your analysis, then certainly, limiting yourself to referencing just the small area will make things easier and more accurate. If you absolutely need to work the entire 20x15km at once, then splitting it first and then trying to stitch it together later will make everything a lot more painful going forward.
In short: Do not put all your faith and trust into statistical numbers such as RMS. All these are just indicators that allow you to better understand your work, they are NOT qualifiers of any kind. Indicators such as these always need interpretation and consideration of context. There's a reason there's a whole field of science revolving around this, after all ;) . Also, trust your eyes: If the result of a transformation looks good (good fitting to the map/reference material), the result IS good! The benefit of working with visual data is that we are allowed to trust our visual senses. Human brains are very hard to beat at pattern and outlier recognition.