You may have resolved the problem with your timing chain by now, but just to let you know I had the same problem for my 1Series 180d. I contacted BMW direct and they gave me 100% parts and the garage reduced their labour by €15 (about £20) per hour. This was out of warranty, but only had 54000 miles and was 2007. It still cost €1850 but that was still a lot less than you were quoting.
Suggest you try your luck with BMW and see what they will offer. From reading other websites, I have come to the conclusion that there is a fault in the crankshaft which causes the timing chain to go. Have you ever heard that?