My dd refused a paci until 11 weeks, and started taking it then only when she was tired and ready to fall asleep. I had the same concern you do about starting to give it so late, but it was my saviour in starting to help teach her independent sleep. Prior to that we were a serious AP case of rocking/walking/jiggling to sleep, but once she took the paci, I could put her into her crib drowsy and she started to get used to falling asleep in her crib on her own. Shortly after that she started sucking her fingers a lot more, and found her thumb, and once I knews she could get it in her mouth when she needed to, I stopped using the paci entirely (@ 3 weeks after I had started).
Re w2s, it worked twice for me by holding down during the jolts, but no more after that - I tried for about 10 days. Pat/shhh used to just infuriate my dd, and I never persisted with it.
What worked for me was focusing on A time (impossible to read cues apart from when it was too late), consistent nap time wind down, going in to her only if her cries were escalating (vs mantra cry which I only learned to distinguish for my dd at 3 months or talking to herself).
For my own sanity, I also stopped spending hours in her room trying to get her back to sleep. I gave it a time of limit of trying for max 20 minutes, then up, adjust A time accordingly and back down again. I decided on a routine, and saw it as guideline re sleep/something to strive towards, but stopped getting too stressed if my dd didn't sleep according to plan. I took each day at a time re naps, and adjusted her schedule accordingly depending on how she napped during the day, although I kept feeding times fixed (formula fed and could go 4 hrs from 12 weeks). I also read "Healthy Sleep Habits, Happy Child" which provides an excellent explanation of how babies evolve into their sleep habits, and my dd's routine was set up to allow for the development of her morning nap first, and then naps 2 & 3. This meant I went to an EASYA...EASYA routine which worked much better for us. She is doing really well now, but I just need to stay on top of her routine as her A times change, and if for some reason she has a bad nap here or there.
Having said all of this, it does seem like some los just are short nappers. I guess an early indication of this would be if you've tried all the things Stacy mentioned, and timed her am nap to fall around 9am for a couple of weeks and she still doesn't go beyond 45 mins after 4/5 months, it's possible she's a short napper, since the morning nap is the first to be established by 4 months.
I hope some of this helps...I guess my question to you is: has your dd showed any signs of thumb/finger sucking or other self soothing method? I think ss is one of the key factors in getting los to sleep independently.
Best of luck to you!