This worked for both my babies and they are VERY good sleepers. My oldest slept through from 3 months and my youngest from 3 weeks!!!
No a/c. My oldest slept in our room. When I was on my own she'd sleep 4 hours but with hubby home she would only sleep 2 hours. It took me a few weeks to realise that I don't sleep with a/c unless he is home!
Own room. My oldest slept in the hallway as we didn't have a room for her. My youngest sleep in the guest room. I found that I woke them up and they woke me up. If they woke me up I always gave them a feed although they could do without.
Always feed in the dark and only change the nappy if they pooped. Change in as dark room as possible and don't say a word. Make it really boring!
Don't stress and hurry up the feeds during the day. The more food they get during the day the less they need at night. It felt like I just fed the baby all day long. It gets better when they start solids!
I agree that she is too young for controlled crying. All babies are different and I found that mine fell into their own sleeping pattern all by them selves. Books can be a bit much. Believe in your own intuition as a mother!