He is only 13 months. IMO, dropping bottles isn't a big deal right at one.
From reading your posts, you have 2 things you are trying to change - from bottles to cups and then you are trying to drop a bottle.
I never focused on dropping bottles. This will happen as they eat more food. What I did do was change from formula to whole milk. I did give my son the toddler formula for a while and I would offer him whole milk during the day. That was one issue.
Then the switch from bottles to sippy. They will all turn down milk in cups if they know you will give in and put it in a bottle. Both of mine did this. I was all in a panic until one day I really did forget my DD's bottle at home when I dropped her off to grandma's. I pick her up and she was drinking the milk fine. Her grandma just told her that there weren't any bottles at her house and if she wanted to drink milk she had to out of the sippy. She did.
Anyway, I have had more problems with straw sippys then I would like to talk about. What worked for us was a soft tip Nuby sippy. Whatever you use, just put the milk in there and be done with it. He will tantrum if you have given in to the bottles in the past.
Right now, though I think you are changing too much. Decide what are you tackling first? Off formula to whole milk. Off bottles to cups. Go with one first. Give yourself some slack too. He is only 13 months. My son's milk intake went down after solids on its own. Now my son asks for milk and might drink about 20oz or more a day and he has a healthy appetite. I don't find it to be an issue.