It's harder to sleep when congested - and my other first thought was to ask whether reflux is an issue. If there's reflux, she might be feeling an acid burn when she goes horizontal; that's what happened w/my DD1, and WOW, was that ever a steep learning curve! Had I known what to look for sooner, DD's getting upset by our wind-down routine would have clued me in that she didn't WANT to be flat in her cot.
A couple random thoughts:
For night wakings, is it possible to send DH in to her for one of the night wakings (maybe try this weekend when he's not working?) so she doesn't smell milk? She might be less inclined to demand a feed if she doesn't smell milk. Send him in with the paci and see how he gets on.
I would also suggest trying to keep that 5AM waking very low-key: if she's hungry, feed her (or yes, try a paci) and then put her back down as if it's a night waking.
What's her personality? If she's Touchy, she may not like the pat/shh. Both mine HATED it.
If she's asking to eat again during an A time, could be a number of things, but again, in our case it was looking to soothe the reflux burn (milk soothes the acid burn, so she'd nurse just enough to get some milk, feel better, and then stop nursing since she wasn't hungry - drove me around the bend since I didn't understand that). She may also just have a strong need to suck *something* (this was my DD2, who lived with her paci till 2-1/2YO).
If the regular wind-down gets her riled up, switch it up: maybe try playing in her room, not even leaving it for the first A time, and when she can barely hold her eyes open, THEN put her down.
You mentioned she slept well in the Moby and again napped ON you; this also suggests reflux to me. I got to the point before we sorted the reflux where I tried to get mine to take at least ONE nap on me so we could BOTH get some rest! (They stopped agreeing to do that around 3 months, so enjoy it now.