For starters, you bought a USED BMW WITHOUT A WARRANTY. Yes the car originally sold for 76k but you bought a car that lost most of its value since it is implied(the used car resale value) that it WILL NEED repairs. Look at how Lexus SUVs hold their value of the equivalent year and this is attributed to less anticipated costly repairs, hence it holds its value better. You're going to pay one way or another.

Sure you got unlucky. I know you said you knew the original owner but did they know how to properly warm up the car or how to cool off the turbos before shutting it off(taking it easy that last stretch.)

Complaining on these forums is like putting your wallet in your mouth. No one cares. The forum people are advising you to go to a BMW independent shop as the transmission may need to get serviced instead of replaced. At least call them and talk to them like an adult. The dealer doesn't care for small jobs, they just want to replace your transmission without even considering any alternative.