An edge guided router bit would be great!
On with a ball bearing roller on the tip.
When you cut the frame down, the door will not fit in the frame the same as before. This could cause problems with hinge load bearing and latching problems.
The best solution is to use lattice strips or handmade rips behind the casing.
If you need to, you can use shims to fine tune the width you need. Clear caulking will hide a multitude of sin when it's on the edge of dark stained trim.
On painted casings, Caulk the cracks and paint it. Use the router on the side of the frame opposite the hinges and latch.