ML is correct.
If your mems sensors are hitting a physical limit, they will no longer
produce a correct average
due to clipping.

The typical solution to your problem is having an accelerometer with
sufficient dynamic range that it
does not clip, and low pass filter the heck out of it. Then use a rate gyro
to get your dynamic tilt.
Combine the two signals to get a noise free tilt signal. LPF accel+ HPF
gyro at same break point.
Given your extreme vibration, you will want to find a gryo with the lowest
acceleration induced errors.

See the 'composite filter' techniques used in the DIY Segway software.

Robert
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