L.A.
Is she sleeping on her tummy? Can she lift her head?
Make sure you sleep with her crib sheets and blankets before you use them in her crib. Consider a fan or a white noise machine.. The swing makes a ticking noise, maybe lay her in the crib but have the swing going next to her to hear that rhythmic sound.
Place her in the crib with her head up against the corner of the bumper.
When you do all of the night time feedings, changing and burping, do it in as much darkness as possible, do not speak and do not make eye contact with her. The other thing we realized is that the wipes were cold, we purchased ans then used a wipe warmer and poof, it worked like a charm, none of that startle from the cold wipes.
You sound hesitant about the binky. With the binky, do you just go ahead and give it to her right away or do you have her cry for it? Some infants really just need that binky to sooth. I would automatically give it to her and not wait for the crying. It just gets her all riled up and harder to calm down. Follow her lead on that.
I know you just want sleep. You are also realizing her needs are very different from your first 2, just follow her lead with no preconceived ideas.
I am sending you good sleep very soon..