I was in the exact same boat. No room at all. I ended up using the fishing line method with a pair of loops and pulled hard and it finally popped out enough for me to get my hands on it to rip it the rest of the way out.
I really think that people do not realize the force it takes to get these things out at first. You really try to baby it and that just doesn't work.
Current: 2014 F10 M5
Previous: 2015 F80 M3, 2013 E92 M3, 2013 F10 M5, 2009 E90 M3, 1998 E36 M3