Sorry, somehow I missed this - probably couldn't reply when I read it, then it wasn't "new", so I forgot.
You can fit it there, but it is not perfect. I suppose if you get some stuff to put in the empty space, it might work. With the canvas off, if you mean to use the more recent one...
On the newer one, I believe the top hay part is SLIGHTLY wider than the wagon - though it can be forced in.