ThisWould be worth looking at the water pump. These generally weren't a problem like the M50/52 but it is 22 years old so it's possible that the impeller's broken up or is slipping on the shaft.
Also try flushing the radiator out.
Just for my own curiosity... would the radiator still become hot to the touch, or does the water pump not working mean the radiator would still be ambient/cold?To add more detail to my example of a failed impeller- I agree with @smorris_12 direction on this
Car would idle fine, there was basic flow of fluid around the system and I checked this looking at the pipes going in and out of the heater matrix inside the car (at the bulkhead)
But… when the car drove, it over heated. Straight into the red
Get your pump pulled out