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.
Member, Extropy Institute