I think it will work.Make sure your bottom threshold is tight to the door. The other areas around the door can always be built out with an added weatherstrip installed. The other issue may be the strike plate, but like I said if you need to add a 1/4 inch piece of wood on that side the whole way, you can make it work. then add weatherstrip to the outside, they sell pieces with a build out and stop , like for garage overhead doors.
The door now, how much of a gap is there around it ?
Hope it works out, at least if you do not cut into the door you can return it, make sure of that for sure.