Thank you so much for that link, it looks like it may be very helpful.
I wouldn't recommend trying cold-turkey just to get her to drink all the milk you know she needs from a bottle.
I really don't think that I have the heart to do this anyway. I'm pretty sure it would be a really horrible experience for the both of us and I would most likely give in.
I have tried the syringe, she's less fond of that than of the bottle. I have also tried a cup and I think I might be able to get that to work if I could find the right cup. The problem is that she's trying to hold onto everything and shove it in her mouth so when I cup feed her we end up spilling most of the milk. I will try it again though, can't hurt!