Oh, I left a visit off!
The 335i has twin turbos. The coolant goes through the oil filter tower. This was visit 2.5. We think (they think) that oil from the tower managed to get into the coolant system thus degrading the hoses.
Total damage was about $2,800.
As for DIY, I'll attempt, and enjoy, working on any of my other vehicles. The BMW, no freak'n way. Too many special fitments, tools, and other stuff required. Worse yet, they tend to throw up error codes in series, that is problem A identified (fix A), problem B now identified (fix B), problem C now identified (fix C), ...