The issue is not in the bit depth, the displacement texture attached in the first message has only few shades of grey, increasing bit depth won't help in a slightest. The problem is this texture is pushing Corona displacement too hard. You need to blur it slightly, so displacement would have some room to work nicely. The more variance between neighbouring pixels the texture will have, the more chances for artifacts in displacement will be. You can try to reduce displacement size in render settings to combat that, but it has its limits - eventually increased parsing time and RAM consumption will make this solution impractical.
I would also suggest to consider using Corona pattern instead displacement - i think it would be more preferable solution in your case.