DD2 just turned a year last week, and I am about to make this change as well. Like yours, she is still on 3 bottles (6 oz each). I have decided to first transition to milk in the bottle, by slowly replacing an oz of formula for an oz of milk until it is all milk over the course of a couple of weeks. Then, I will tackle the issue of the bottle versus sippy cup. I want to get her used to the taste of the milk first.
However, just in the past day or two, she has taken to grabbing the bottle out of my hands and holding it herself, but only after spending 5-10 minutes playing games with it, turning it upside down and letting it drip etc. If she keeps that up, the bottle is going to disappear cold turkey, I think.
Only thing I keep waffling on is whether to keep that mid day bottle or drop it right away and replace with milk in a sippy and a snack, like you are considering. She really loves that mid day bottle....