When trying to use one of the tools with the Super Tools mod, for example the pickaxe, it says "You need the right tool for this job".
How do I add these tools to be recognized as legitimate tools with the natural progression mod?

Sorry for the impractically late reply - it's been a busy year+ and NatProg has been on life-support until now. You just need to add these tools to the tag natprog:considered_as_axe or natprog:considered_as_pickaxe