So the bottom of the outlet has the constant power. To make sure I understand:
1. Unscrew the bottom white, bottom black, and ground
2. Cut a piece of new white wire and strip both ends
3. Wire nut together, the old bottom white wire, new white from New Romex, and one end of white that is stripped at both ends
4. Connect the other end of the spliced white to the bottom silver screw
5. Cut a piece of new black wire and strip both ends
6. Wire nut together, the old bottom black wire, the new black wire from romex, and one end of the spliced piece of black
7. Connect the other end of the spliced black section to the bottom brass screw
8. Cut a segment of ground and strip both ends
9. Wire nut the old ground, new ground from romex, and one end of piece of ground.
6 Connect the other free end of the sliced piece of ground to the green screw