The other possible issue could be how you use your slab roller. You have to make smaller compressions as you, as well as roll in both direction instead of just one. On large pieces, I roll way past the width and length I need, and cut my piece out of the center. The ends and sides are the weakest, so I avoid cutting tiles on the edge of the slab.
Good point. There have been numerous discussions here about rolling out slabs, especially those that are large. Many, who work a lot with slabs will flip and rotate their clay slabs in between rolling. In other words, they partially thin it with the roller, then rotate it 90 degrees, as well as turn the entire slab over. This is done with each successive pass. That way slab is receiving the same amount of pressure all around.
I don't work with large slabs, so I cannot say how well this prevents cracking/ breaking. Just to be safe, I even do it with my smaller slabs, everything from several inches by several inches to slabs that are even smaller.