This has probably been covered in the past but could not locate a link. I am unsure how to reline the doors if it is possible or is there something else wrong that would be causing it to push out. The font and top seem to be correct but the bottom back lip seems to be the problem. I attached a photo so you can see the issue. Thanks for the help.
Your door has a little twist in it. Common problem. Believe it or not but the way to "fix" it is as follows. Place a block of wood between the door and the jam near the top of the door, about where the latch is. Then push in on the very bottom back edge where the skin and inner frame come together. Go slowly and check fit often.