Do you have "power" turned on? It makes the throttle really jerky/stabby. Try with it off.
In terms of the "bucking" below 3K, sounds like you are coming off the throttle too quickly. Try to be more smooth, I think all powerful cars these days are like this. If I did that on my E46 M it would be pretty jerky.
To alleviate some of your concern, this really does not sound like a gearbox malfunction.
///M Power - 2011.75 LMB M3 6MT (fuelly)