I think the scale of your typical results is too coarse to show if there is a systematic offset. The histogram suggests there is a systematic offset of 400uV but you would not be able to see that on the typical graph you have shown - less than the thickness of the graph line. Try expanding that graph to see if there is a small offset (I assume there is).
Also, I would suggest you use a DC analysis for checking the offset, not a transient analysis, so you can separate out dynamic behavior from static behavior.
Keith.