I'm biased toward bread, and willing to fire over the course of days, so I'm probably not the one to reassure you.
On the other hand, I've baked off four dozen loaves with retained heat from a single firing, so that's what I mean by "lots of bread".
You could plan to have an *extra* thickness of insulation board underneath the saputo, to be removed and replaced if you need the mass. That is, your dome would sit on sufficient insulation, then you'd stack more insulation inside the walls to put the tiles at your planned final height floor height.
I ended up adding 4.5" of brick to my floor (beyond the 2.25" of a standard Pompeii build) for bread; the final floor is 6.75" thick. I had planned for the possibility, so my dome and door heights were workable either way.