OK I'm not sure you will want to hear this but really, if she is getting up between 9.30-10am in the mornings, then there is no wonder she is never asleep before 9.30-10pm! Expecting her to go to bed between 7-9pm is likely just too early given her wakeup time & that she napped 3-4pm & hence why an earlier bedtime is not working.
I do think eliminating the feeding to sleep & teaching her to become an independent sleeper will help, especially with reducing night wakings, but I think perhaps restructuring her daytime routine so she is properly tired for bedtime would be a good starting point. If, once you have done this, she is still taking forever to settle and waking repeatedly at night you could then tackle the weaning.
I would suggest a more appropriate routine for her age would be something like:
Wake: 7am
Nap: 12.30-2/2.30 (I'd say at this age she should be having around 2hrs day sleep, maybe 1.5hrs but not less)
Bed: 7/7.30pm
or if you are owls & like a lie in you could shift it all 1hr later & do
Wake: 8am
Nap: 1.30-3/3.30
Bed: 8/8.30pm
By shifting her morning wakeup time and her nap earlier, she should be more ready for bed at 7-8pm & so it should take significantly less time to settle her.
What do you think? Would you be willing to wake her up earlier in the mornings in order to achieve this?
If you want to give it a try, I would wake her 15mins earlier every few days, very gradually so she has time to get used to it, rather than shocking her by waking her up at 7am when she's gone to bed at midnight the night before! As you wake her earlier, she will also need her nap moving gradually earlier & same with bedtime.