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>>However, you would still need to know where the horizontal or vertical was or to level the inclinometer.  I’m told that this is possible electronically with MEMS technology and is used in smart phones.  <

I used to work with such MEMS tilt sensors.  Something for this application would typically be two MEMS accelerometers mounted orthongonally.  From the ratio of their outputs you can determine the gravitational vector.  But the accuracy of the result was dependent upon lots of factors.  The zero or null offset when an accelerometer was horizontal, the linearity of the output over the range of motion, the scale factor accuracy, how well matched the two sensors are, and the noise component of the signal.  Added to this was the time and temperature stability of each of the above.

I haven't looked at the specs for such devices for a long while, but I don't recall in the past that any affordable units could realistically achieve the sub arc minute type of precision for a wide range of motion under field conditions.  What might be closer to being feasible is a MEMS sensor that was accurate for a very small range around zero degrees from the vertical.

Don Seltzer