One caution about using a grinder for rubs... if you have sugar in it, it can quickly turn to a super-fine powder. I threw some granulated sugar in my grinder a few weeks ago, and it became almost a cloud of sugar dust, it was so fine. If you use it to break up the clumps, I'd do it very, very quickly.
Same principle is also true for salt. I use kosher salt and if I put it in the grinder, it almost immediately turns it into that same cloud of fine powder.
Since I like my salt and sugar to have some substance to it, I no longer use a grinder. But try it out and let us know how it works for you.