S., I can't offer you any specific advice. It's easy to say stop and let them cry it out but not every child responds well to that tactic. I can tell you this from experience. My older two were easy to get back to sleep with the firm "no" and a pat on the back. I have a little one now who does NOT respond to it well. I've let him cry it out for over an hour with an occasional pat on the back and it does NOT work. He is not quite two and still nursing. I know there's no need for it and it's a comfort thing for him because he can lay down and not need "boo" in order to go sleep. It's the middle of the night that's a killer.
What I do is let him fuss for a bit before I get up. I don't rush to his side in hopes that he will settle down on his own. This rarely happens but once in a great while it does. Normally, he just gets madder and madder until he's hyperventilating (same with a soft touch but no boo). I'm not about to have it out for an hour every night and distract the rest of the family so I give in for the sake of everyone else. Thankfully, he's down to waking up once a night, sometimes not until 5 or 6 a.m. (YAY!)
So if the water or sugar-free drink doesn't work, if filling the cup less and less with milk doesn't work, if patting the back doesn't work, and you're getting mroe stressed, don't fret too much. This is a temporary thing your child will outgrow. I would suggest brushing his or her teeth well in the morning if you still do stick with the milk to help prevent cavities. Perhaps you could get the child to drink a little bit of water at the end to wash out the milk left in the mouth. That would help cut down on the development of cavities, too.