Steve,

The cascade control formerly used I presume was a single input-single output (SISO) structure for each loop.

Since there are three thermistors located at VERY interesting places in the thermal structure, why not consider building a multiple input-multiple output (MIMO) controller. I suspect that making use of all three sensors simultaneously to control each thermal energy source will enable the inner thermistor to attain zero SSE before the system as a whole has reached a steady state. That is to say the transient temperatures and energy flow will be working their way from the inside to the outside.

Pusuing the implementation a little bit more - a measured temperature difference across a homogeneous material (for which you know the thermal conductivity) tells you a lot about the rate of heat flow and if the assembly has a fair amount of symmetry, temperatures could be projected based on calculated heat flow rates. So, if heat flows can be calculated and temperatures projected, why not calculate yet again to determine what change to a heat flow you'd like to have in order to acquire a different temperature. Since Peltier heat flow is well understood given the current through it and the delta T across it, now you can change the heat pumping capability of the Peltier element by calculating a new current value based on the desired heat flow.

My apologies for being so detailed, but I think you've got a better than average chance of achieving the desired performance given the sensors and locations described.

Bruce