Cleanup on cement is easy, just push it in the hole. If it was me there and easy shot you'd be lucky if there was handful on the ground.
With something like that though you'd end pushing it all down the chute with a broom one hundred pounds at a time and it would make a mess and take quite a long time. Of all the setups I ever went top that had it at the back of the gargae only one ever made it and it was nut coal. The opening was right in the floor too so it was as low as possible.
Like I said going through the door wouldn't be much of a problem from what I can see. Just be sure to let them know they need to across grass. Once it dries up you don't mess it up much unless it's really soft.