I'm looking for a material that is durable, can be acquired in bulk,
can withstand 700 degress C, and that conducts heat less well at
higher temperatures than at lower temperatures. That is: the thermal
conductivity has an inverse relationship with temperature.

look at macor. You haven't specified over what temperature range you'd
like your specific thermal conductivity to drop or by how much.

Kaye and Laby Tables of physical and chemical Constants 16 the edition
page 90 gives thermal conductivities of of refactory materials.
Alumina seems to suit your requirements Lambda (W/m/degree kelvin) =
11 at 773 degrees K and 6 at 1773 degrees Kelvin.