Great idea about searing meat and then grinding it.  You'll also want to make
sure that your grinder is sanitized.  I've never tried grinding meat in a food
processor.  I know it doesn't work well for pemmican.  I picked up a hand
operated grinder a few years ago for about $25.  It is adjustable from very
coarse to very fine grind.  It also has an attachment for making paleo sausage.