Putting baby down "drowsy but awake"?

Hello, all! My little one will be 4 months on Friday and since she turned 3 months, I've been trying to do all those "right" things and get her to sleep more independently. Pretty much the whole internet tells me I should be putting her down drowsy but awake and then soothing her back to sleep without picking her up. Please, please tell me how on earth you made this happen and at what age?

As background, she's been a snugglebunny since birth. We co-sleep at night because she refused to sleep without being held when she was born and she's always liked nursing herself to sleep. I've had limited and hard-won success getting her to sleep in her crib for naps, though the swing still works best.

However, for the last couple of weeks, she will always wake up 25 or 45 minutes after we put her down. This is in the swing, in a dimmed room, while swaddled, with white noise. I'm getting almost nothing done anymore, hence my sudden desire to try get her to self-soothe. Maybe she just got an early start on her 4-month regression. However, she needs two two-hour naps to stay a happy baby all day, and it is extremely difficult to get her to go back to sleep once she wakes up unless I lie down with her.

I have spent several hours of several days in a row trying to put her down while at varying degrees of awake and invariably she becomes completely alert and starts crying within 5 minutes. Usually, she commences fussing as soon as she sees that we're holding her over the crib mattress or swing, before we've even started to actually put her down! She will do this indefinitely until I lose patience and just nurse/bounce her to sleep. When she wakes up, same deal if we try to soothe her without picking her up. Even putting my arms entirely around her while in her crib and/or jiggling her is not good enough--she insists on being picked up and held and bounced and preferably nursed. My husband can sooth her down without the latter, but it takes 2-3 times as long. We've never been able to get her to accept a pacifier.

I generally operate off the principle that my baby is not a freak, so I'm hoping that some of you here had similar experiences! Did it just take many weeks of slow progress? Did it not work till they were a little older?