I loved the idea of less and less milk in the cup for several nights ~ brilliant!
I, too, went through the same thing with my daughter at that age and I was also pregnant. I sometimes would quietly cry at her beside (in the dark, mind you) as I was so tired. Finally, I just told her she had the option of water and nothing else. I chose water because she didn't want it. We had one night of hysterical crying where I went back in my room, turned down the monitor, and would doze for 10 mins, checking in when I'd wake. I went in a few times to reiterate that we weren't drinking at night and even started naming people (my husband, her grandmother, her friends) and telling her that they were all sleeping and would drink in the morning. She eventually got so tired she fell asleep, and the next night she was so *overtired* that she slept through the night.
Good luck to you ~ it's a common stage but it's an ugly one. There's no easy way past it but you are right to try and nip it in the bud while you still have one. Be strong and the few hours of broken sleep will yield better times.
Hugs,
L.