After adding a part to the correct slot you will notice that several "Missing" parts will also be added, these must be removed to manually add the Sub parts that should be there manually one by one.

Alternatively you can attach the part that is closest to the Torso you want and then once landed on the map use the Dev tool "Fix world prosthesis" in the Dev mode button that is 4th from the left (5th if using Awesome Inventory).

I do not use Prepare Carefully but I don't see why it would not also work.