Any of our site sponsor will be able to do the job.
https://www.bmw-sg.com/forums/categories/bmw-specialist-workshops-and-servicing.165/
I personally only tried 2 from the list (excluding PML). I went for the basic ws and not those performance enhancing ws, but it should not matter, all of them are fully capable and fairly priced, just spend some time/effort to visit and ask them DIRECTLY before making a decision
Seals, solenoids are part of the full mechatronic
Cheapest - change seal (less than S$100 for parts only)
Next - change solenoids (less than S$800 for parts only)
Wow - change the full mechatronics (S$3.2k++++ include labour, depend on ws)
Logically it would be (in terms of cost) to try the cheapest solution and then move up the next stage.
If you have the budget and want a piece of mind and save time, just change the whole mechatronics, because it WILL include all the seals, solenoids, in its original factory fitted condition, no worries about whether your ws will install the individual parts properly or not.
I tried the step-by-step approach (in spite of ws telling me to change the whole set). Cost me about S$2K (for seals and solenoids + labour) + 3-4 days(x2) downtime. Unfortunately the improved 'new drive' feeling only lasted 6 months and the problems came back
(mine was similar to yours, but progressed to high rev before switching gears, followed by 'transmission failure' message on iDrive, before I made the S$2K repair)
In a way, I regretted doing the step by step method of diagnosis, as by the time I felt that enough is enough as it was almost unbearable to drive, my COE only left 1 year. As my ws commented, change the whole thing now, at least enjoy the ride BMW is supposed to drive for the remaining COE period.
Ultimately it is your judgement of cost/savings vs peace of mind. Good luck!