There is the obvious, visit at the time of year that will provide you with more interesting skies! Any time during the dry season, you are going to struggle with good light and the atmospheric dust will always produce the overcast looking skies.
Dropping in skies becomes a challenge, as you need to match the vegetation colour/seasonality with the sky.
I would tend to edit more in PS, where use of luminosity masks provide the ability to edit in finer details around the mid-tone contrasts. This does allow you to extract more of the detail in a more subtle manner. It also allows you to get that golden light look with pushing the image too hard with sliders and also moving the white balance too high.
In my experience, it looks likes the adjustment of the global white balance is turning your sky more grey. I appreciate that you are new to digital editing, though I see 3 different white balance zones across the image. Camera's really struggle in African animalscape type images.
1. The sky would benefit from a selection and a cooler WB. Adjust it to give a slight bluish look, that would provide colour contrast against the vegetation/grey elephant.
2. I would not warm the dry grasses behind the elephants, I think the colour balance works well in the original image. It is starting to look a little fake.
3. I would add a touch of warmth to elephant and greens in the foreground, where your focus is.
You are also blowing out the whites on the cattle egret with your editing. I appreciate it adds to the scene, though you need to watch out for this.
In scenes like these, I have resorted to using linear profiles for each of my cameras. This is maybe slightly more advanced, though the tone curve in lightroom will push certain colours and raise the brightness of a RAW file. It allows you to build an image more subtly, that may otherwise appear lost.
In terms of camera techs, it looks like you have used a focal range between 100-200mm. You can also get away with shooting closer to F4 at those focal lengths and still having subject focus. This would have given more BOKEH to assist with the background.
A depth mask and background blur would reduce the prominence of the background and sky.