MPU6050 accel/gyro noise that behaves strangely - what might be doing this?
Errors look like +/-256 +/- expected drift. 

This suggests some kind of synchronising error - such as reading the LSByte of one sample and the MSByte of the next or vice versa. How does your gyro handle this, is there some way to temporarily put it on hold while you read data? 

Also, examine the raw data around a few of these errors to see if it happens when a slowly drifting signal crosses an MSByte boundary. Obviously, focus on the Y Gyro, the errors are most clearly separated from the noise.