So just another quick thought while I have a second-
If she is consistent with waking at 30 min have you tried Wake 2 Sleep?
I'm not good at attaching links, but I know somewhere it is described perfectly.
Basically you go in about 10-15 min before you know she is going to wake and put your hand on her, like her chest or cheek just to get her to stir and then she stays asleep. I know this sounds super scary b/c she already is not sleeping, but it helps her move into the next sleep cycle without waking.
Also, consistently 30 min naps could start as UT (under tired)
Have you taken a day lately and just logged exactly what her day looks like? If you could do that and post it for us that would help us see some clues that may help you.
Also, I can tell you from experience that this is not a quick easy fix, but it is a worthwhile fix. I know it is easier to just do what makes it good for the moment, but you will only be extending your problems. Sometimes we do have to AP to get naps etc... but to truly make it work, we have to stick to the plan as much as we can.
One more thing, she is right now not used to self soothing so you could gently start her. What I mean is you can't put her WIDE awake directly in her bed after falling asleep in your nice warm arms for the last 4 mo. So start by cuddling and shh/patting in your arms and as her eyes start to flutter closed or she gets the stare, lay her in the bed while still shhh/patting.
I'm not sure what problem to tackle first-NW or naps, but you can also use shhh/pat at night when she wakes instead of feeding. She may not really be hungry if she is taking all of her full feeds. Do you have a partner who could go to your LO at night and try to resettle her? If it is you going to her, she will be thinking YUM FOOD!!! I know with her slow weight gain you may not be game for this, but you are having A Lot of NW at this point and I am not 100% convinced they are necessary
HTH-I think your first plan of action would be to map her day if you have not already done that. Also, hope I did not sound too strong...just want to help b/c I know it is worth the time and effort