Please post a picture of whatever you find, for educational purposes, when you get to it. That is quite a lot of play.
Taking the wheel off goes very quickly, by the way.
I put the bike up on it's center stand on top of a piece of wood, (I found a slab 2.25" thick was sufficient for my 2012 C5 with 18" rear) Pull the cotter pin and remove the axle nut. Pull the axle out, catching the long spacer. Separate the wheel from the brake drum/ sprocket. My wheel requires a bit of worrying, but with that amount of slop, your's should come off easily.
Pulling the brake drum is only a bit more work from this point. So far, I have found work on my RE goes much quicker and easier than any other motorcycle I've ever worked on.