Welcome to BW forums
Let me see if I can answer a couple of your issues
i am trying to go through the transition to 4 hour easy as suggested in the book
Not all babies move to 4hrly E at 4 months. If she can then fine, if not don't panic, you can make the move slowly or hold off on shifting the E times until she's a bit older. You would still need to look at her A times as these effect how tired she is for naps and if the A time isn't increased suitably it can lead to short napping.
Dream feeds never worked
What you are doing is fine. Not everyone does the DF, the idea is that everyone gets more sleep but if you go to bed earlier and do NFs instead, no problem.
shhhh-pat worked, but it did! It took a good 15 minutes but she slept.
This is absolutely normal. It takes 20 mins to fall to sleep so actually 15 mins is good.
we end up with more of a sshhh-pat battle!
This could be related to her routine. If you could post your actual routine times (not the guidance times from the book but what actually happens in your day) we can have a look and see if something needs a tweak for you. We use a format like this on the forums:
WU (wake up) 7.00
E
A 1hr
S 8.00 - 8.40 (resettled in arms with shush/pat)
S 9.00 - 9.40
E 10
A 1hr... and so on
include a few notes about her mood or what happened, how you settled her
include
BT (bed time)
and
NF (night feed ) and NW (night waking not for a feed)
The times that she does cry I pick her up and sssh-pat her on my shoulder where she will eventually fall asleep.
This could be where you need to make a change. Rather than shush/patting to sleep over your shoulder you need to get her nice and sleepy but shift the position, horizontal in arms continue to shush/pat and then lay in the cot and continue to shush/pat either to sleep or to drowsy. Then you keep reducing the shush/pat in the cot at each sleep so that you gradually reduce whilst still offering support when needed.
She also wakes up after 40 minutes so thats another round of ssshhh-pat to get her back to sleep!
You can begin your shush/pat earlier so that she doesn't fully wake, This is called W2S (wake to sleep) here's a link:
https://babywhispererforums.com/index.php?topic=223809.040 min naps can be because LO has not learned to transition from one sleep cycle to the next, the W2S can help to teach this.
40 min naps can also be linked to the routine, we'll be able to see where they are happening in your EASY when you post it.
So I'm asking how long would you expect it to take to get a baby on EASY starting from scratch?
It's very individual depending on the LO, the age, any health problems, and the approach parents take. it is relatively easy to get "stuck" in one place rather than keep moving forward with the sleep training so it can then take longer.
My own DS I tried to implement independent sleep from day 1 (although didn't really know how and didn't discover BW until he was 4 wks old) and he was going to sleep independently at around 8 weeks - that doesn't mean he never needed any further help ever again, it just means that when he was on the right routine he had learned how to go to sleep after a wind down and being put in his bed, I left the room and he fell to sleep alone, I even got a smile before sleep some times. So for us 2 months.
Hope this helps