There's another alternative. Don't buy ground meat. Buy larger pieces and cut them into about 3/4-inch to 1-inch dice and then chop them in the food processor. Here's how:
Get your pork, veal, and beef and cut them all about the same size 3/4-inch to 1-inch works well. Don't buy pre-cut meat (like stew meat) as the pieces will generally be of different sizes and you'll end up with more work.
Once the meat is diced, mix all the pieces together and put them in the refrigerator for a couple-three hours. You want the meat to be cold. You can also put the food processor blade(s) and the bowl into the freezer or refrigerator.
When the meat is sufficiently cold, put it into the food processor, but be sure not to overfill or overload the bowl. For a pound of meat process in two or three batches, maybe even four depending on the size of your food processor. IOW, work in small batches. PULSE the meat. As the meat is processed, it will blend together, and generally no additional mixing is necessary.
Be sure the blades in your machine are sharp. I sharpen mine two or three times a year, and have one blade that is dedicated to processing meat. It's never used for nuts, vegetables (especially hard vegetables), grains, seeds ... just meat. The blade stays sharper longer.
So, equal sized dice, cold meat, small batches, PULSE, sharp and preferably cold, stainless steel blade(s).