Hi there, thanks a lot for your detailed video :) I saw another video where the tensioner had a torx socket. I saw my 2005 e87 has a pin (like yours in the video) so this has saved me some confusion.
I had the same issue, everything you explain are on point but belt came in too short. My car is 116i 2005 and as it seems the belt that I should use is 6pk1870. I can’t get it to wrap around every crank even if I pin the tension. Do you have any idea what causes this problem?
There are only 2 possible issues, belt is to short or you are going round the pulley in a slightly different way which seems correct but is not, has happened to me in more than one occasion. Just try fitting the old belt back, if it fits then your belt is short.
