I think you are under on the steel. Just my 2 cents.
My slab is 2 sheets of mesh ,bar right around the edge & doubled up in the corners .I brought bar up out of the slab then bent it around & joined it to run up through the block wall & joined it again to bar right around the perimeter.
I can I suggest that you put bar up through the block,tie it to bar running right around the perimeter of the block & pour concrete into the block.This will help spread & support your hearth slab & whatever goes on top of it. The blocks I have were cast with a channel in the top for exactly that purpose,you could cut out a bit 2'' x 2'' in each block so you can trowel finish the top of the concrete.
This is my oven .I hate to think what it weighs all up.