You need to exclude one of these to prevent combustion.
Your system has fuel (straw) - you are aiming to keep both air and heat away from it. The straw can char if it gets sufficiently hot, even with the absence of air.
Without knowing a lot of details about your design, I suspect that your cob wall between the fire and the insulation is too thin (hence your straw is overheating), and there is an air leak somewhere. Cob cracks when drying so you might need to hunt around for it.
Personally I wouldn't use clay-slip and straw for this application for precisely this reason. Too many opportunities for failure. On the plus side, your oven will likely still work fine even with the insulation partially charred away. It may just be a bit less efficient.