Good news, I found and fixed the problem! It was a bad DAC (AD7524) in the CV generation path that was causing this. In the test procedure that waveform:blue described here the DAC seemed fine, but the malfunction was concerning only one of the switches inside the DAC. These switches (8 of them, each flipped by one of 8 bits) determine the final output of the DAC and when only one of them fails, the DAC output looks almost normal but is shifted (especially when a switch on the MSB side fails). This caused all the symptoms. I read somewhere this DAC is very sensitive to PSU failure, so that has probably caused it in our cases. In my case, there was some corrosion on the powerconnector to the mainboard which led to unstable supply to the mainboard.
For general info: I've replaced the DAC (AD7524) with a PM7524F which works fine. A TLC7524 should also work. Different brand, same function.
ps. Also posted this in the gearslutz thread, as the info might be of value to others