OK, I don't know if this is "in line" with child-led weaning or not, but here's what I would do.....
When my DD was around 20 months old, she began some of that behavior. It was completely unacceptable to me, so I began to instill some nursing limits. I wanted her to know when I would say yes, and when I would say no. I don't know if you are already doing this, but it sounds like you are not. I think that predictablilty and consistency alone would probably help a LOT of the behavior problems with regards to nursing.
I decided that DD could nurse upon waking, before & after nap, once in the afternoon, and before bed. So I picked one block of time to work on - the easiest for us was the time from when she woke up to nap time. If she asked to nurse, I'd reply that she could nurse at sleepy time, and offer her food, water, and cuddles instead. Then she could nurse on request for the rest of the day. We did that for about 3-4 weeks before I moved onto the next time block. So we worked on it very slowly. I also included night-weaning in all of that.
She wasn't all that thrilled about the process, but once she got used to it, she was fine and so was I. It was so much nicer to be able to say "you can have Na Na again at _____ time" and not have a meltdown over it. And, I feel that in the long run, we would be able to nurse longer because of it.
And I must say that a few months after we got our routine down, she became quite ill for 3 weeks, and then she was teething, and then we were moving. So, upon the onset of her illness, I had resumed nursing her as much as I could, including at night. We JUST completed our move about 2 weeks ago, and I am planning to start setting those limits again - slowly of course.
Of course, I recently posted about my own dilema about the possibility of weaning. I had hoped to let DD wean herself.