I would have to say that a trip to the dump is in order if you have that much trash laying around. I understand how much it can pile up when moving, but it needs to go.
He didn't get that big by being stupid, if you secure your trash (or get rid of it) and there are other food sources nearby that are easy to get to he will go where the easy food sources are. Right now, your trash is the easy food source. As long as you leave it out in an area that has bears this will be an ongoing problem, even if you shoot this particular bear. You need a good long term solution.
You will also need to electrify your coop. If he is determined to get in, he will, but again you just need to make it harder for him to get to them than the easy pickings up the street.