Been doing that very same thing since I got my grinder last year. I cut them into strips just a little bit smaller than the throat of my grinder. Auger grabs it and just draws the whole thing in easy peasy.....
1) I lay the strips on a cookie pan and flash chill them in the freezer before grinding (not frozen, but dang near)
2) After mixing in spices and even letting the 1st grind sit overnight, if I'm going for a 2nd grind, I like to shape the 1st grind into long rough "logs" and again put them on the cookie pan for a flash chill to near frozen. They work just like the strips of whole meat do. I rarely have to use the stomper when doing it this way. The "logs" may separate as it's not a solid piece of meat, but it still wants to fall down the throat of the grinder neck by gravity.
My mom's great-uncle ran a small butcher shop back in the 60's-70's. Her cousin worked for him after school, weekends and summers...... After having lengthy discussions with him about how and why they did certain things, he said one of the benefits to chunking-up the meat was they would pre-season the meat, chill it over night, then grind/stuff it all at once...... It took less time to process everything that way...... ShoneyBoy