As part of decades of work as an instrument designer, I've worked with literally hundreds of installations involving temperature control, including troubleshooting. The deeply theoretical work I did in University is not particularly useful in this kind of situation- it's more critical thinking with a bit (okay, quite a lot) of hands-on Engineering knowledge. I've also designed a number of lines of temperature controllers, digital, analog and processor-based, so I do know what I speak of and I know where the instrument specifications come from (since I wrote them!). The one I'm working on now is capable of doing (censored) single digit MICRO degrees stability over hours. It's tested in an environmental chamber over a wide range.
I'm not sure whether you're using a bad instrument/sensor, misusing a good instrument/sensor, or misinterpreting the specifications, but something bad is clearly going down at your place and it sounds like it's costing money.
"R type" refers to a thermocouple (Platinum/Platinum-Rhodium 13%), useful mostly at very high temperatures. I doubt you have or want those, they have very tiny output (< 10uV/K vs. more like 55 for type J).
An RTD is often used at relatively low temperatures when you need better than a degree C or two stability, and response speed (which impacts control robustness and response to disturbances) and mechanical ruggedness are relatively unimportant. The electronic design for 3 wire RTDs or 4 wire RTDs is quite straightforward.
So, why not throw out the thermocouples and replace them with RTDs?
This sounds like a seriously bad situation you have, honestly.
Best regards, Spehro Pefhany