How can I trim out the gap along a new exterior door with a smaller rough opening?
I agree with S Rura.  The only way to do this without messing with the siding is to install a nice trim or brickmold.  You will need to install a plywood filler to match the depth from your rough framing to the siding level.  Caulk all the seams. Then install some ripped(if necessary) brickmold or other flat trim like painted pine, MDF, or PVC. Then caulk the seams around the door and J-channel again.  It will look great. On the inside, just extend the drywall, tape and mud, then install the trim of your choice.