Any of our trusted site sponsors should be able to sort out the problems with regards to gear box or the transmission.
From what I understand (layman terms), the gear setup is made up of 2 components, the transmission and the mechanical gears (at least for my E60)
Mechanical gears probably last about 250k km before need to overhaul them. The transmission unit is about 200k km
Transmission would consist of the mechatronics which include the solenoids. Normally if just vibrate during initial move off (like what i experienced previously), the 1st-2nd solenoids that controls the 1st-2nd gear shift are going to kaput soon. I dont get this when I'm cruising on highway.
You could try the cheaper solution of just changing the solenoids (about $700+ at ES) + labour (depends on WS) or the whole mechatronics(which would include the solenoids) Mine is using the ZF transmission which is pretty robust, so I only changed the solenoids. No vibration at low gears now.
Whole mechatronic change would cost about S$3.2K at one of the site sponsor (does not include ATF) or S$2300+ at ES
The above was all based on my personal experience with my E60 so do take note of that.
Another culprit could be the speed control sensor located within the mechatronic but not sure whether you can just change that alone.
My opinion would be that if your ride has at least 3-4 years left and you would want to take it all the way, do the full mechatronics change, or if you have budget, + the mechanical gears as well.
Good luck!
(PS. if any of the gurus think that any of my above info is wrong, please correct me, as I'm always keen to know more, thx!)