This will give me a nice insulating outer surface (4" thick), and I'll fill the space with loose fill vermiculite. This is a cheap and easy insulating option - you can see the bags of vermiculite stacked up on the left hand side below, ready to go in.
I'm tipping the loose vermiculite into this gap - this will eventually fill up all this space. I've filled all the cracks in the dome with powdered fireclay, and have coated the whole dome with ~1/4" of dry fireclay. You can just see this in the picture below. The idea is that this will sift into any cracks that form in future and fill them up - a good tip from Alan Scotts book, if I remember right.