I just had a thought about your GF's lack of libido, which she thinks is due to her BC method. If you take the job and she doesn't move with you, she does not need to be on BC (not sure why she is on it now since you two are not having sex anyway). She can go off it with no worries about pregnancy. Then she can see if she recovers (or develops) a libido. Of course this may not work - because 1. she needs the BC for medical, not pregnancy control, reasons (and if so, why has she talked about being willing to go off it?), or 2. she is asexual. If she is asexual, she is never going to be interested in sex with you, so maybe this is something she should figure out now? If she does develop a libido, this may let her realise that it is you she is not hot about, not men in general. In which case a better life opens up for both of you.
Seriously, you worry so much about her, but this present situation hurts her as much as it hurts you, just not in as obvious a way. If you really care about her so much, set her free to find a partner that suits her better. I really mean this, my Ex (we were married a long time) didn't want me to leave, but he has a new partner now and they are much better suited to each other than we were.
In other words, GO and on your own!!!!!