Do you think it's possible to cut the door jamb and move the cowl in? Since it's at the bottom the work won't be so obvious. Having completely replacing my cowls and fitting new doors, bending the hinges is something I would avoid at all cost.
The 2x4 trick is something you can try, but unless you have experience with this technique I'd go pretty slow with it and it's going to take a bit of effort to get it to move that much. Remember that the door is going to pivot at the other hinge so the whole door is going to move outward from the top hinge down.
In case you haven't seen this,
HERE'S a picture of the hinge bending technique.
Personally, I'd cut the cowl.
