H.B.
I'm going through this with my daughter too. She's 11 months. I don't think it's quite as bad as yours though. She will go to sleep without a problem during the day but I've had to go up and give her back her paci a few times lately at night (she only gets to have it in bed). I never had to do that before and twice she woke up screaming and wouldn't go back down for a long time. She mostly does it when she is tired but it seems to be getting worse.
I can't just plop her down to do chores like some moms have suggested because she can walk and she grabs hold of my leg and won't let go. When I can get her to not hold on to me, I let her get into the tupperware drawers and that keeps her busy. I'm not doing the sling thing either; she weighs about 23lbs and I'm 115 so she is just too heavy to carry around like that, plus she grabs at anything within reach. I have to take her to the bathroom with me also, but I keep some toys in there for her and that keeps her busy while I take care of business; I'm also using the opportunity to teach her some potty training words and explain what I'm doing and let her watch while I flush--I know sounds gross but maybe she'll get the idea so it'll be easier to potty train later.
Sometimes I just have to let her cry. I try to keep those moments brief and reassure her as soon as I get back into the room. And sometimes, I just let her hang all over me and pray that this will pass quickly! If I learn any good tricks, I'll let you know.