A Transformation and a Question

I was at the beauty shop last week not getting my hair cut....well, that sounds crazy doesn't it?  :)  I'm trying to let my hair grow a bit since I kept it a couple of inches long all summer and now it's getting cold out and so is my neck.  I remember years ago my husband's grandmother saying in the car, "Close the window, the breeze is making my neck cold."  I thought that was the craziest thing until I got to be, well the age I am now.  Anyway, while not getting my hair cut I was sitting in a chair waiting and had my feet on a small stool the beautician keeps there for short people to put their feet on while drying their hair.  I commented that I needed a stool like that in my bedroom but hadn't had any luck finding one.  I just wanted a small used one I could recover and the flea  market I'd been to the week before was fresh out.  Or maybe they'd never had one, what do I know.  To make this long story a bit shorter she gave me one she had but couldn't use because it didn't slide under the dryer chair - too tall.  What do you think?

Not bad, right?  It's a little taller than I wanted but it works....I have a rocker there where I like to sit in the mornings doing my Bible study and prayer time.  Now the only things I've ever recovered have been chairs and they were easy peasy.  Turn them over, remove the screws holding the padded seat on, put new fabric on, staple it underneath, put the seat back on the chair, put the screws back in, turn the chair right side up and there you have it.  Much to my surprise....I turn this stool over and there are no screws.  Nary a one.  I have no idea how that padded top is held on there.  No.  Idea.  So I improvised and made a "throw" for the top.  I love this fabric - it's part of a line of fabric I also used on my pillow shams.

And since I'm a quilter at heart, not a reupholsterer (is that a word because on my screen it's underlined in red), I quilted the top.

Now for the question part of this post.  The corners stick out.  It's not horrible but I wanted them to drape.  Are they sticking out because I put batting in the whole thing?  Or for some other unknown reason?  And whatever the reason is there a way to fix that?  Without taking the whole thing apart I mean.  Because I'm pretty sure I'm not going to take it apart.  Hmmm, not pretty sure, real sure.