Turned some more aluminium and rivets in to a bottom frame:

A calcium silicate plate (usually used for thermal insulation of fireplaces, for example) cut with a jigsaw, fits nicely:

This material can withstand very high temperatures (it was quite unimpressed by a blowtorch) and is very easy to cut and drill, but it's also a bit delicate and brittle.

Here's the aluminium plate that will end up on top of all that. It will be heated by the carbon resistors: