I'd love to be able to give you some magic advise that worked with my eldest, but sorry I don't have any
I read things like "I'm really loathe to muck about with the basic bedtime routine because I think it works" and know exactly where you come from. We thought certain things were right and what babies should do, like bedtime in a cot upstairs early evening. In fact in insisting on this when it clearly wasn't happening, for us, it created many more far worse sleep associations (like the picking up/rocking/shushing) while we tried to shoe-horn a square into a circular hole.
I'd just stop all that worrying about must have a bedtime and just be kind to yourself (and baby and DH) and do what's easiest for a bit, in order to break the sleep associations. Have a week sitting on sofa with breast in mouth all evening. Or sitting in bouncy chair holding dummy in mouth. Whatever is easiest for now.
Then having broken the rocking/shushing habit, start bedtime routine again once you have a sleep trigger that you know works so she can self settle. We started bedtime with DD only when I knew she would lie still with dummy in her mouth and suck it for 10 minutes or so to get to sleep. If she was doing this at 4 weeks, I'd have started bedtime at 4 weeks. If it took to 7 months, I'd have been happy waiting until 7 months. As it happened she was about 14 weeks when she learnt to self settle using a dummy.
Other self settle sleep triggers:
- Sucking (dummy, fingers)
- Tickling (hand? Like in In The Night Garden)
- Hair twiddling (or just head holding as a baby - DC3 did this)
- Patting (DC2 used to do this. Patting him developed to him patting Ted)
There'll be loads others I haven't thought of. Key is something child can do without you.
Honestly, I would abandon rocking to sleep because it's not teaching her to self settle.