>> after trimming it carefully with pliers
Can you say more about how you even off the broken pots? Do you use pliers to break off parts by grabbing and bending them outwards, or what?
How do you control where the clay breaks?
I would have guessed something like a hacksaw and a file would be needed to get a straight or smooth edge. Like cutting glass, maybe: scratch or saw a groove, and then expect the fracture to follow the groove.
