No need even for a big magnet....
....just grains of magnetite in the clay. or hematite.
This is how I'd do it:
Take a hematite rich clay. Maybe add finely powederd magnetite. Or better yet, something slightly more exotic: illmentite or one of the paramagnetic minerals.
Mold or carve a cool shape.
As you say, put it in a kiln and cook it above the Currie point of all these minerals.
Then, let it cool in within a directed magnetic field. This could be done with a strong magnet or in an electric coil. As it cools in the magnetic field, the magnetic domains line up and you have a lodestone.
Red clays typically have excellent paleomagnetic signals. Whole careers have been built upon the paleomagnetic properties of "redbeds".