As you may be aware, the BW philosophy does not encourage CIO in any form, as it causes the LO to lose trust in the caregiver. Tracy always said there was a gentler solution to the problem, it was up to us to find it. I'm sure you'll find that if you get her routine and any prop issues sorted, she'll settle on her own and the NWs will also improve. It's clear with the 30 minute naps that she is OT. When they have short naps, you need to decrease the following A time to compensate. Extending a short nap will help immensely, but isn't always possible. Pat/shh is a great tool for that, but babies this age may not respond well to it. PU/PD is another tool that you could use, and certainly that's one for those NWs after 3 am, instead of CIO. W2S is another great tool, I've never used it personally, but lots of people have success with it. The key is to pick your method and be consistent. Are there any prop issues that you're aware of?
An earlier bedtime will also help, since she's got 4 hours of A time during that last block, which is just too long at this age unless you can fit another 30 minute nap in there somewhere. It's great that she's happy during the day, though, it certainly makes it easier!
HTH, let me know how you make out!