What I mean about a cinder block base is this:
That image comes from the
Forno Bravo oven plans. It's a good read.
The layers, from top to bottom:
exterior stucco
insulation
thermal mass (brick, cob)
oven air space (where the pizza goes)
fire brick base (under the pizza)
Insulation base (wine bottles in cob, or cement fireboard)
steel sheet where all of that ^^^ rests
cinder block stand
foundation
ground
Here is an example of a test oven I made. It's not a perfect match for yours but I hope it gets the idea across: