Thermal probe is placed inside the copper die which is between resistor and container. Measuring container bottom is not the right way to go which can be seen from those ansys pictures too

Is that red area the dryice level which is why upper from there container starts to get warmer or whats the reason for it?

And about silver container, i dont think its worth a try. Any inpurities will often result in loss of heat conducting properties and practically this means youll propably need to have very pure silver to get pass 99,99 copper. Im not sure how does silver heat conducting improve in cold temps but copper has this property too. I would definetly concentrate on designing copper containers instead of changing material to silver

Have you made comparisons with same size old school wide flat bottom and cone/stepper type bottoms with that program Cpt.Planet?

Nice to notice that some people still finds this stuff intresting!