Hi Mom101,
Not sure you are going to like what I have to say, but there is no miracle fix, Paige was also waking up 2-3 times a night for milk and at around 13 months I realized it was just habit and not hunger and I , like you, was also very tired.
I am a bit of a softy and not into crying etc, but I just decided no more milk before 5 am, She gets bottle at bedtime and then one in the morning when she wakes up and that is it.
It took a few nights, when she did wake up I would go cuddle, offer juice, rock her and like you say it would take a long time and when you are tired that is the last thing you feel like doing, but after a few nights she got the message that she was not going to get her own way and started sleeping so much better.
I suggest you tell your little girl there is no more milk and stick to it, don't give in no matter how much she cries, that doesn't mean you have to leave her, you can console her, cuddle etc, but she needs to know you mean business. Hopefully like my daughter she will get the message after a few days and give up on night time feeds
Good luck