Coincidence, I'm working on the same problem.
I also presumed a bad coolant circulation pump. I tested it after removing it from the car and all test were OK doK. After putting it back, I still had the same problem. Time for a new coolant circulation pump.
Same problem with the new pump, so I have to look somewhere else.
After opening the old pump, I noticed a lot of rust around the electrical motor.
Maybe that rust prevented to pump to turn, although the electrical circuit appeared to be OK.
I'm told that a defective pump could destroy the climate control module, creating all sorts of problems.
Anyone with a suggestion or two????