The only element to warp badly was the roof. The warping happened as the pieces were drying out, mainly due to lack of space and not regular enough turning.
The Muffle is designed to slot together and not to need any other fixing. However it is important to me that it is as air tight as possible for the firings, so I sealed the seams with clay and clamming.
When the muffle was assembled in the kiln, I gave it 2 coats of batt wash to protect it a bit from the corrosive atmosphere in the kiln.