i2c_t3 | Enhanced I2C library for Teensy 3.x devices

I have an arduino based device (Teensy 3.2) and I am trying to read data from a H3LIS331DL accelerometer breakout board. I can write to the control registers on the accelerometer and read from the data registers, but I'm having trouble getting stable, useful data.

First, useful data. The data sheet for the acclelerometer chip just says for the data registers "X-axis acceleration data. The value is expressed as two’s complement." The SparkFun LIS331 library says "The data that comes out is 12-bit data, left justified, so the lower four bits of the data are always zero." If the data is 12 bits per axis I would guess that the output (properly conditioned) should be 0-4095 with zero Gs being at something like 2048, but this doesn't match what I'm getting. With the accelerometer sitting still at my desk right now the X and Y axes are giving readings at the high and low end (either 0-19 or 4063-4095) and the Z axis is giving readings from 9-80 (always below 2048 in any orientation).

Are my expectations for the data wrong, or am I doing something to not be getting the correct data?

Second, stable data. The low setting on this accelerometer is +/- 100G range. My current bench testing is at -1G to +1G (1% of the full range), so I would expect the output data to have proportionally small range, but the output range just from a constant position is already almost 2% of the full scale.

What can I do to get more stable output data?