I dont know if this will help but it was the same situation my sister was in with her daughter. She woke every 3 hours, and no matter what she tried refused to go back to sleep unless she was given milk (slightly different to you though but as she was obsessed with milk it was her calming tool). She took a trip to our gp, she was a reflux baby and it turns out was still suffering at this age, went back on zantac and just about instantly started sleeping properly again. Two weeks later went back downhill, back to gp and she put her on a nasal spray (nasonex i think), saying some children's passages are underdeveloped still and cause sleep problems, it worked literally overnight and she has slept up to 13hrs a night since.

Personally, my DD1 had a thing for 4am, I could hear her chatting away to herself until she started getting cranky, I would give her a bottle of milk and walk back out, she would drink and put herself back to sleep. I was told she was hungry and unable to make it through the night still (she was a huge eater of solids and milk during the day). I learnt if I didnt give her the bottle, this was her morning wake up time, when I gave her the bottle, she went back to sleep until 9.