I'm using a Cabella's branded meat grinder. I think it's a half horse, 6 pound per minute, number 8 die model. Seems to work really well. On the first grind with a medium die, it'll run about as fast as a person can feed it. The second grind with a medium die takes more work to feed, but I've never heard the motor strain. I paid about $330 on sale for this model several years ago, even though it is a bit of overkill for what I do.
Regarding your food processor. Do you chill the meat to slightly frozen between passes through your food processor? I'm wondering if running really cold, less sticky, meat would be easier on your food processor. A second approach might be to add some water to the meat with every pass through the food processor.