There is no way automated digital way to completely eliminate the pencil lines without doing some damage to the quality of the ink lines. However, it is possible to get close—probably close enough that you could manually fix the problems in a few minutes using a graphics tablet.
Looking at the sample image, it appears that there are two characteristics that could allow a computer to differentiate the pencil from the ink. First, the pencil lines are mostly a lighter shade of grey. Second, the pencil lines are thinner. In signal/image processing terms (what Photoshop effects are really doing behind the scenes), these properties correspond to amplitude and frequency.
Your original approach (using brightness and contrast settings) only took into account the first property. By picking the one that works best, or combining both, it is possible to get a fairly good result that only requires minimal touch-up.
'Lightness' of the Line (Amplitude)
The histogram of the image shows us the relative number of pixels at each brightness level (shades of grey). In the figure below I have labeled some of the features on the histogram of your example image. The pull-out below the histogram is a black-and-white (binary) image showing all the pixels that have brightness levels in the indicated region on the histogram. This mostly corresponds to the pencil lines, but as you can see, it also contains part of the soft edge of the ink lines. When I remove all the pixels with brightness levels in that region, I get the image on the left. As you can see, most of the pencil is gone, but now the edges of the ink lines look a little rough. If I had moved the threshold (cut-off point on the histogram) further to the left, it would have gotten rid of more of the very light pencil markings, but it would have also degraded the ink lines even more.
'Thinness' of the Line (Frequency)
Manipulating the frequency content of an image is done all the time in graphics editing, but relatively few people realize what they are doing, because Photoshop hides all the technical details behind what they call a blur filter.
If I apply a Gaussian Blur filter to your image (using a radius of 2 px) and then apply a levels adjustment, I get the image in the figure below. As you can see, the resulting lines are mostly free of pencil markings, but they are thicker and have less detail than your original ink lines. That is what a blur filter does: it removes detail. This is useful to you because thin lines = higher level of detail and your pencil lines are usually thinner than your ink lines.
The Final Image
Every image is different, and the only way to figure out what will work best is to experiment. When I played around with your example image, I seemed to get better results from the second (blur) method. However, I suspect that given enough time, the best results would come from some combination of the two. I will end with a figure showing a sequence of image adjustments that gave me fairly good results after a few minutes, but that could use more fine-tuning.