That’s quite some hot air balloon though. It’s a heck of a lot of air to heat, even if by only one degree.
And then what? The sphere would barely float (since I presume 1320 must be the absolute minimum size), lose heat to its environment, and drift back down again.
Playing devil’s advocate, I suppose a sphere based on a greenhouse effect could achieve a temperature gradient of 1 degree with its environment using sunlight only. But still, you wouldn’t want a metallic material for such a sphere – you need something transparent and insulating – and that’s what the OP is about.
Really hard to follow some of this stuff, but what I want to know, given that there is technology to manufacture “foamed” metal is if we are closer to a reasonable solution for the OPs requirements by using a foamed metal skin (closed cell for vacuum retention) of say 50% density.
My guess is that there would be 8 times the resistance to buckling.