Transition away from formula and bottles

I read that around this time it's good to begin transitioining away from using bottles. Makes sense to me!

Ever since we returned from Europe, I've slowly been increasing the percentage of whole milk (organic) into her formula. It's been going really well! Right now the mix is 2 oz formula and 8 of milk. We're down to 3 bottles/day (first thing in the AM, after lunch, and at bedtime).

Sabrina has been drinking out of sippy cups for about 3 months now for water so I figured it should be easy to just start using sippy cups for her milk. Well, apparently Sabrina has grown quite fond of her bottle. Last night I used a brand new sippy cup (new brand) that is insulated and leak-proof and offered it to her in the usual bedtime routine we have established. She played with it for a while, sipped on it, but that was it. I thought maybe she wasn't that hungry because she had eaten well that day. So this morning I offered her the same kind of sippy cup, knowing she was hungry. She refused, cried, pushed it away, etc.

I even pretended to drink from it since she seems to imitate everything I do (just this morning I looked over at her while I was putting lotion on my arms and she was doing the same motions LOL). Even that failed. She was getting crankier with time and I started feeling bad that she must be really hungry. So I took her down to the kitchen and poured the stuff into the kind of sippy cup she has been using (for water) and took her back upstairs to offer it to her. She drank it but I think the issue is that it flows out much more slowly than the bottle nipples do and she was getting frustrated.

So if I have time I'm going to go to the store to see if they have any kind of faster flowing sippy cups.