It sounds like you and the repairman are missing something worn or broken in the drive train (from clutch to head). I see you have verified most or all needed item items to be in working conditions.

My suggestions:

1. Remove the shaft and cable to the trimmer's head. Start the trimmer and add resistance with a wooden rod. Check the square shaft connection close (on shaft, in clutch) for wear and torque with the wooden rod. Verify you have torque going to the head by pressing against the rod with it running.

2. If the power at the head and clutch tested OK. Manually test the cable and string head by forcing resistance between the two (vise and hands or vise-grips and hands).

3. If the cable and string's head checks OK. Make cure the cable is seated in the clutch and string heads. With manual torque if a small screw driver or etc will let you hold the clutch and manually torq head.

Good Luck, loger

PS. Post pics of possible problems if needed.