Aha it might be the sprocket then, I recently changed the sprocket nut for the larger one. I will double check the free play at the sprocket side, if yours is moving that much then thats where my slop is coming from.Ill have a look tonight.
To hopefully put your mind at rest you could see what a few other bikes feel like when on a centre stand and rocking the back wheel. (Best to ask permission first or you might get attacked ). I know you said it didn't do it before the sprocket change, which is a bit worrying, but it is easy to kid yourself when you become super sensitive to a possible problem. Good luck.
Was that in gear Darrsi?