Will she tolerate a swaddle? That might help with the jolting.
Can you try for the first A time just staying in her room and playing with her there, watching her cues to see when she starts to get tired, and see if you can stretch it maybe 10 minutes past that super-low-key and put her down drowsy if not all the way asleep for now. When I did that with J, I turned off her overhead light around an hour and then I put on some soft music and just held her in dim light (we had a small IKEA light on her wall that was barely more than night-light strength for when we went in at night), and when she couldn't hold her eyes open any more, I held her for an extra minute or two and in she went.