The uncontrolled pitch up scenario is familiar to me from an emergency procedure on another aircraft and this procedure may well have utility (with suitable modifications) on a wide range of transport aircraft (The pitch trim systems are similar). I am providing this procedure strictly as a discussion tool to stimulate thought and not recommending it for any aircraft type.
From the A-4 Natops Manual (Please ignore the partial disconnect details)
Nose Pitchup on Takeoff
Nose pitchup on takeoff may be due to either runaway noseup trim or partial disconnect of the elevator power system. Specific procedures to counter either of these malfunctions are published in this emergency procedures section, but the pilot must react successfully to the immediate problem of nose pitchup to maintain control of the aircraft and provide time for determination of the exact nature of the malfunction. Limited forward stick travel, in the case of partial disconnect, and limited elevator effectiveness, in the case of runaway noseup trim, cause excessive nose pitchup as the aircraft accelerates through 170 KIAS and the flaps are raised.
To regain control of the aircraft the pilot must immediately lower the flaps while reducing airspeed to the minimum required for safe flight by maintaining a controllable climbing attitude and adjusting the power setting as necessary. The judicious use of bank angle may be advantageous and necessary in assisting the pilot to control nose high attitude. (NA. reference to jettison of external stores) Once controlled flight is ensured, the pilot shall comply with the applicable emergency procedures………(END OF APPLICABLE PORTION OF PARAGRAPH)