I just wanted to let you know that I have the same problem with my 23 wk old DD. We've worked through issues w/in the last week by taking away her dummy and reflux. But, despite the reflux she's a happy baby. I have a similar situation where she wakes anywhere from 4:30 to 6:00 happy, takes short naps (happy) and fights her catnap. I struggle as well with doing pu/pd or shh/pat at 4:30am since it can take an hour to make a happy baby mad enough to go through the whole cycle of pu/pd. (Its hard to make a happy baby mad, and I'm too tired.) I've started leaving her in her cot to let her play, and only go in if she starts crying. She will often go back to sleep for a little while. I think there's a danger of making them unhappy in their cot if you go in when they are happy. (I think I read this in the BW book.) I would suggest staying home in the morning until you can eliminate the early wake-ups. My DD always wants to fall asleep before I get home at 8:30 from taking my DS to preschool...which sets us up for a bad day. (The morning nap seems to set the tone for the day.) The catnap is a struggle for us as well, but I would do whatever you can to get her to sleep. The days I don't keep at it, she is so OT by bedtime that she fusses until I can get her to bed, and then we have the early wake-ups. Today, as I'm typing, she's having her catnap, and it was a real fight. I think she just had to shut the world out and cry. Pu/pd didn't help at all, I ended up with a hand on her to let her know I was there, and she eventually cried herself to sleep. We're seeing progress with her everyday, and I think we are close to sorting her out.
The moderators will probably have some great advise for you, but I'd work on the am nap and if you think she is tired definitely do what you have to, to get her to catnap. I think its really important for the long term to let her play in her cot if she's happy. My DS (3yrs) has always been like that, and it is a godsend. From about a year old we would leave toys and books in his cot and we could get up to an extra hour of sleep!
Good luck...