The other thing to do is to dissolve as much as will dissolve in boiling water, and filter it hot--since the solubility of NaCl is very similar at RT and at 100 deg C, it will precipitate out of solution when boiling (or will not have dissolved to begin with). That means that your solution has a much higher concentration of KCl than NaCl. Then you can boil the solution you just filtered some more until more NaCl precipitates out (from water loss due to boiling--you're concentrating the solution). Reapeat the process until you're happy.
Of course, the easiest way to do this is to go to the supermarket or hardware store and ask for 'non-sodium' water softener tablets. I bought a 40-lb. bag of pure KCl for about $4 at a supermarket.