I'm having difficulty with this stage. I can't get the subtlety you have on the normal texturing. I've used multiple resol...

This answer might come a little late for you, but maybe this'll be of use to someone ...

*sigh* Accidentally posted before I'd finished (can't seem to edit/delete comments). Right - your problem, quite possibly, is that you may have saved your bump texture with an 8-bit color depth. If the image has an 8-bit color depth, the range of grey hues available will be EXTREMELY limited and ensure that you get the braille-bump effect you're describing. Simply save your bump texture image with a 16-bit color depth - then reload the image (you can either do this in the UV Image editor, or in the Texture tab of the Properties window) and you should now find that your texture painting is considerably smoother - particularly when at very low strengths when the limited range of hues is greatly emphasized. As a final point, you might also want to increase the 'Bump Mapping > Method' to "Best Quality" - also in the Texture tab of the Properties window, under 'Influence'. The difference won't be as substantial as the bit-depth distinction, but it is a visible improvement over the default "Low Quality". Hope that helps.

Wow, thank you. That was the issue. I'm glad I came back to check on this. Hopefully this will help others as well.