I found some information on advanced dewar construction in Richard Rhodes book "Dark Sun: the making of the Hydrogen bomb. I don't know if the cryonics companies are aware of this or not (probably) but I thought I'd mention it.
...Between the second, outer assembly and the dewar, the
cryogenicists ingeniously interposed a single floating thermal
radiation shield-another thin walled tank, probably made of
copper...
... a thermal-radiation shield floating in a vacuum can
significantly reduce radiant-heat transport from a warm exterior to
a cold interior. Without it Wechsler observes "your talking a warm
surface and a cold surface, and the temperature difference is a
couple hundred degrees Kelvin. I don't care if you've got a vacuum
between them, the heat leak into the cold surface is serious. But
theres a neat little trick. If you can put in a surface with an
intermediate temperature and float it-isolate it thermally- then
the outside surface sees the intermediate, and the inside one sees
the other side of the intermediate, and that cuts the loss way
down...
...rather than clutter the secondary with multiple floating
shields, they borrowed another trick, if you can make a shield
float at a lower temperature than it normally would, Wechsler says,
than you pick up the reflectivity of fifty thermal radiation
shields. To cool the shield they welded a pan to the bottom of the
copper shield that they kept filled with liquid nitrogen.....
hope this is of use.
Brian
Member, Extropy Institute