I knew what you meant...trying to fluff it while it was still laid out wide. I've seen guys try to do this and barely had any results with a wheel rake.
What I tried to imply was that you'll probably have to pay "more" after the trade in of your rake on a wheel rake. Take that same money and purchase a tedder.....you'll be WAY ahead. I fought the urge to buy a tedder for years. After I got one, I absolutely could not believe the difference.
There is an art to running a tedder. One setting does not fit all, especially in alfalfa. With pure grass hay you can pretty much run as fast as you want and sling it as far as you want. With legumes, you have to speed up the tractor and slow down the rpm's of the tedder in order to not knock off the leaves.
Good luck with whatever you decide to do. Hey, let us know how the wheel rake works to fluff your hay if you go that route.