I decided to "adjust" the temperature sensor...
stripped it down again
the plan was to "simply" saw 1/3" or so off the sealed end,
so the thermocouple would hang in the middle of the oven
took a hacksaw to it - no effect
looks like it's stainless steel
tried a Dremel with one of the little "parting" discs
knife through butter!
cleaned the end with the same disc
so now have a slightly shorter tube
with thermostat out in the open
tried a profile run last night
MUCH closer to the first graph (several posts ago)
close enough that the dead time seems to have gone away
so next step is to look at stirring PID control into the equation(s)
modified probe and resultant profile shown below