16 month old sleeps very late and wakes up all throughout the night, we are tired

Our 16 month old has never been a very consistent sleeper but the last few weeks it's gone sharply downhill. Her naps stop after 3pm and she usually sleeps at 10pm-1am. She wakes anytime from 9-10am. It takes roughly 30-50 minutes of bouncing and rocking for her to sleep. all the while she thrashes around in our arms. Without this she just screams. After this she will wake up anytime after, sometimes 15 minutes after sometimes four hours, but she never sleeps through the night. She will often wake up multiple times in the night, staying awake anywhere from 20 minutes to several hours. Lately we have tried the "camp out" method trying to decrease contact with her in an attempt to make her a more independent sleeper. This has not been successful so far, as she quickly gets to the point where she is red faced, and breathing very shallow from how intensely she cries. There is often no in-between, at night she is either dead asleep or crying very intensely. This has made the camping out method unviable so far as we have to quit almost right after she wakes up, because patting her and being there for her just isnt enough. After letting her cry for even just a short while she is inconsolable for awhile. Anything else we can try? Desperate for possible solutions. Thanks