To try to increase the strength of the resistors I replaced the clay with plaster. I mixed 5/8 of a teaspoon plaster of Paris with  1/8 of a teaspoon powdered graphite and 3/4 of a teaspoon water. I poured it into a narrow rectangular mould about 1/4 of an inch wide by 1 1/4 inches long and embedded leads. When I removed it from the mould in the morning there were two problems. Firstly it was actually likely weaker than the clay ones. Secondly and more importantly its resistance read infinite on my multimeter. Back to the drawing board I guess.