Add a Levels layer ...
Red channel 0/1.00/215 and 0/255
Green channel 0/1.00/225 and 0/255
Blue channel 0/1.00/255 and 0/160
Then mask on to the background. You'll find you can allow it to encroach onto the hair a bit, without harm.
I think you need to go a bit closer to them than that, with the lasso selection.
This happens if you click too quickly. If it thinks you've double-clicked, it will close it. Take your time.
At its heart it's this method.
This is an insanely hard edit. It took me half an hour, working on this web-sized file. Allow yourself 2-3 frustrating hours, working on the full-sized file.
Download the PSD file
I know it must think we're labouring this point very painfully, but a good black-and-white conversion really relies on a nice raw edit. Once you have your calibration done and confirmed against prints, let me know and we'll talk about the editing.
Also - VERY IMPORTANT - do this.
Use ReCAL. CheckCAL is kinda silly, because if you go through it and it says you need to ReCAL, then you have to do it again, and you could have just ReCALed in the first place, you know? ReCAL is the time-sensible option.