Once you know the thickness of the door, check with your local door suppliers, not the big box stores. They might be willing to sell you a door sweep that fits. Lowes and Home Depot have door sweeps that might fit. At least you return one of theirs if it does not. ...
Maybe polk at the jam with an awl or something similar to see if the jam is solid or not. Short of replacing the wood with something more solid, you could get a metal plate that you could bolt the bracket to, then screw the plate to the jam, with how ever many screws it takes....