I don't own an offset, but here is another suggestion you might consider.
Cut out the middle section and splice an extension on one of the doors so that when it closes, it slightly overlaps the other door.
For example, cut out the middle section on the smoker. Close both doors. Now, using the middle cut-out piece, weld it to the right side of the left door. You may have to trim it, but get it to where it just touches the left side of the right door. At this point you will have the doors touching and all of the opening space is closed. Since this probably won't fit perfectly, you might consider then splicing on a bar on the right side of the new left door to overlap the left side of the right door.
Hope that makes sense.
This way you don't have to mess with your hinges, etc and should keep the fabrication to a minimum.
My $0.2