Kate - at this point I'd recommend that you get some help with the night wakings. I know that for me being able to send in DH was a literal lifesaver, as I was also dealing with some heavy PPD at the time.
Yes, he had work to go to, but when I reminded him that I was on call 24/7 and I needed a break, he took the hint. On weekends we'd take turns sleeping in in the mornings and spelling each other for naps. Can you each decide to take a night or two, or (as my DH and I did) to each take a portion of the night?
And crazy as it sounds, you may want to (brace yourself) consider giving back the pacifier, or trying it. Natalie was driving us mad with waking for the thing, and then one day she started to work out how to put it BACK IN BY HERSELF!!!!! Now when I put her in her crib with the paci in her mouth, I lay 2-3 more where her hands can grab them if she wakes without one, and so far I've heard her wake from naps and night sleep a couple times and put herself back down once she has it in her mouth. She really is SOOOOO strongly dependent on sucking SOMETHING, and I'd rather have it be THAT than ME, especially now that she's learning to do it herself.
I think I'd also make sure she's getting enough physical activity to tire her out. Is she getting plenty of tummy time? You can put her on her tummy, put a favorite toy in front of her to lure her, and help her by pushing her feet with your hands so she gets the idea of forward motion, and then when she gets the toy she can play with it on her tummy or roll to her side.
I wonder if she's cutting teeth. Josie waited till 7 months before hers finally started popping through, but she'd been chewing on her hands relentlessly for 3 months by then, and Natalie is currently on meds to help relieve the pain of number FOUR (her bottom 2 came in at 4 months and she's working on the top 2). Does it make a difference if you give pain meds 20 minutes before naptime?
Finally, if she will sleep WITH you, maybe for ONE nap a day you might want to do that. I remember when Josie was small and I was so desperate for sleep, I'd lay her on my belly and the two of us would sleep soundly like that for up to THREE HOURS, after which I could handle the rest of the day so much better. (Just remember to pee first!)