I'm not a jet pilot or engineer but..
Has the possibility of a fault with the PF stick been ruled out? Suppose that fault added a constant nose up. Presumably that would cause the THS trim to exagerate the problem? A stuck bit fault in a digital system can appear to add a constant to an otherwise correct value (eg it adds 1,2,4,8,16 etc) but you would hope error detection catches such faults.
Anyway Google finds..
Chapter 5. Flight controls
Airbus A320 Family Non-Normal Notes
5.19. Sidestick unannunciated transducer faults
It is possible for a failed sidestick transducer to cause uncommanded control inputs. If no fault is detected, the result is that the aircraft behaves as if that input had actually been made. Generally, the autopilot will disconnect and any attempt to control the aircraft with the failed sidestick will fail. The aircraft should be recovered with the other sidestick using the takeover button. Keeping this button pressed for 40 seconds will lock out the failed sidestick, and the autopilot can then be re-engaged. The autopilot should not be disconnected in the normal manner as pressing the takeover button will re-introduce the failed sidestick and the uncommanded input; use the FCU instead.