I use slate and unglazed tiles, from the home center store, as pizza/bread stones. I certainly think you could use your pieces of granite just as well. The only thing you have to be sure to do is to make certain it heats up thoroughly. I usually allow my oven to heat an additional 20 minutes or so to ensure my "stones" are hot. My stones "live" in my oven and they seem happy there. The only time I've had a problem with any breaking/cracking is when I've dropped them. I've been doing this for at least 13 years.
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!