the routine looks good and all i can suggest for now is
1. try to extend the 2nd A time to start nap at 1:30 so wake time is at least 3pm
2. move solids up to 5pm to both distract and give her more energy supply to make it to bathtime
3. see how she does without catnap (assuming had 1hr 30 2nd nap) and then adjust bedtime routine accordingly - if you need to during the transition stage move bath and bedtime forward by 15-30 min to avoid overtiredness.
the hope is that through a combo of low key activities (you can try a DVD after solids until bathtime if that works for your lo or a walk outside if the weather is nice...) and distraction you can gradually stretch that last A time over the next 2-3 weeks so that she is easily staying awake from 3-3:30 until bedtime (a lot of kids can start coping with this long last A time because they do a meal, a little activity, a relaxing/fun bath, more food and cuddles and bed) it is not as if she is going to be playing for 3-4 hours which would be exhausting...