I feel I'm letting her down by not finding a way to see these projects through.
One concern I have is that if I managed to see one of these projects through, she might be crushed when she discovers she hasn't practiced her routines and lyrics hard enough, or that nobody buys her greeting cards.
I don't think it is your responsibility to see her projects through. If she asks for specific and reasonable help that you could provide such as a ride to the store or participation in a class, certainly that is reasonable to provide. I do not believe parents have the obligation to make their kid's schemes work or to prevent them from failing (or not succeeding by adult terms).
You said she doesn't respond well to correction or your input, so I would simply stop offering it. While it may look from an adult perspective like she's "failing" if her ideas don't carry to fruition, that may well be a normal and reasonable part of her learning process. We came up with a lot of child led schemes when I was a kid and it would never have occurred to us to make adults responsible for them nor we were really upset when they didn't set the world on fire. It was about the process not the product.
