Well, if you went 135K miles in 2 years. Damn!
That's ALOT of miles. Did you buy it new? And, btw, good thing you didn't use anything other than Premium and NO Ethenol. Ethenol screws up the BMW engines.
Maybe you should consider
1) selling it and buying a 750.
We have a loaded, used 750i with 7,591 miles for $72,990.
They don't have this issue, especially with a V8 engine.
2) Forking out $4800 and seeing how long it lasts you. (I would highly suggest going nowhere else other than the dealer, because this is a dealer issue...regarding the computers/electronics/updates...etc. You are going to bite the bullet, but if anything else messes up, parts are under warranty.
3) Doing nothing. Since you have no apparent driveablity issues or gas mileage loss.
Those are my thoughts.