This video (especially the part starting at 23:20) describes the same problem you have with double integration, which amplifies low frequency noise to unbearable levels quickly. They solve the problem by sensor fusion, effectively using other sensors (like magnetic field sensors and gyroscopes) simultaneously to infer a more robust estimate of the acceleration coming from gravity alone and the acceleration coming from the movement of the sensor.
To help you with the drift from the double integration you could also try a particle filter to estimate the true position of the accelerometer over time. There is an interesting Tech Talk about a more robust version of this idea.
Perhaps you could also use characteristic points in your time series as a kind of position anchor, e.g. if you can infer with some confidence the times when the pivot is lowest (or highest) and just assume a fixed height over ground for these times. Then, instead of an initial value problem resulting in onesided double integration, you would have a boundary value problem, where you can additionally integrate backwards from the next anchor position. This reduces the time where errors can grow down to half of a period.