I was entertaining the thought of putting up an iron rod gate or fence type gate across the garage doors. Not 100% but would slow them down and make more noise, but could buy one of those fake security camera's.
You will have to mount the hasp, vertically, on the door and the strike plate on the header. Some bending and fitting will need to be done to get it to function smoothly. The hasp will need to swing up to engage the strike plate so it can "swing down" to let the door open and slip past the header as the door is pulled up and away.
And, like has been said, if anybody wants in bad enough this will only slow them down a bit. It will also help with insurance though by having it.
Mark
It hinges, so it will fit with no modifications. It will lay flat on the door when unlocked so it will not obstruct opening. A little spendy but it will work for what you want to do.