Ok, so it does sound as though there are a few problems to resolve.
Overtiredness/overstimulation - 4 - 5 hours of daytime sleep is about right amount for your los age. I would limit the time she spends in the jumperoo, or exersaucer and keep activities
really low key, with quiet relaxed interaction only from you. Really begin to study her behaviour, watch her like a hawk, so that you pick up on her sleepy cues yawning can be a sign of
overtiredness in some los. Base her nap times on this information, rather than timing.
Opps my lo has woken, will get back to you later.
Getting her down within 5 mins is really very good, often when they are overtired, it is actually harder to get them to go to sleep, but I hear what you are saying - that you feel she must be exhausted and therefore sleeping straight away. I think it would be good to stick to the same bedtime and wake up time too.
Sleep prep - what you are doing sounds ok.....especially as she falls asleep so quickley,
I presume she is quite relaxed and happy when you are doing this? What makes you think it is not working well? - do you just mean the night time bit?
Accidental parenting -
could you tell me more about this?One thing I am wondering , is that sometimes around the 4 month mark, they are ready to make the change to 4 hour EASY, and if they haven't been transitioned, they can start night waking - (see p.35-36 The Baby Whisperer Solves All Your Problems). This possibly could be the reason for the 45 min naps too, their ability to stay awake increases (2-2.5 hours for a 4 month old), so if they are not up for long, they don't need so much sleep. You can then get caught in a trap - a vicious circle, they haven't had much sleep, so they then get tired again.
I am wondering whether some adjustments in her routine, may help to solve the problem, let me know what you think.