I agree with you that the lack of daytime sleep is probably feeding into the multiple night wakings. If you believe the paci is a prop, you need to either go with it and replug as much as is necessary, or get rid of it entirely. Using it some of the time but not at other times may just be confusing and frustrating for her.
With the wind-down, you need to try and put her down when she is calm/drowsy but awake. If she falls asleep in your arms, she will expect to still feel your arms around her when she enters light sleep, and if she doesn't, then she'll wake up. That's why the emphasis on falling asleep in the cot.
Shush-pat works whether she sleeps on her side, front or back. If she sleeps best on her back, you can pat her shoulder or hip, or just shush with a firm hand on her tummy. With my LO, I would put rolled up blankets in front and behind him to hold him on his side, and pat his back in this position (he was also tightly swaddled). Then when he was sound asleep I could remove the blanket at his back and gently roll him onto his back - although more often, for naps I would just leave him lying on his side as he slept better that way. The official advice is to put babies to sleep on their backs, but many mamas find their babies sleep much better on their bellies - it is your call to make. If you swaddle, obviously she should not be on her belly. If she sleeps on her belly, that will tend to do the same job as the swaddle by controlling the flailing arms and legs somewhat.
EASY as you know is a routine and not a schedule. If she wakes up at 6 or 7am, you can feed at that time and see if she will settle back to sleep (treat the feed as a night feed ie in the dark and quiet, no diaper change), and then offer a small top up feed at wake up time - but if she won't then you just have to start the day's EASY from her wake up time, and adjust nap times and bedtime accordingly. There are so many mums who wish their EASY would start at 8am, but in the end we have to work with what our babies give us!
By all means you can offer both breasts - she will soon let you know whether or not she wants the second!