To make sure I understand correctly, I'll re-state your issue:
"When you power on your plane and leave it sitting still on the ground, the altitude in MP starts at zero but drifts as far as -120m." This (of course) leads to incorrect altitude being displayed in MP when you begin flying.
If I understand the problem correctly, here is my best advice:
1) Set your EKF2 source alt to Baro, if it is not already.
2) If you have done this, and your altitude is drifting to -120m without the plane moving, something is definitely wrong.
A DataFlash log would help us diagnose the problem, but to record it, you need first to set the parameter LOG_DISARMED = 1, and then send us a log demonstrating the altitude-drift problem.