You may want to consider swapping from "demand feeding" to Mummy-led-a-bit-more feeding.
Things like offering some food and water and a cuddle during the day before offering a BF. I think that your DDs clinginess is probably as much separation anxiety as anything else (i.e. I know Mum can't leave me if I have her nipple hostage), and she may actually be OK with lots of cuddles and less feeds.