How to handle existing electrical when adding a partition wall where two existing wall switches exist?
Let's answer the second question first (quoting from your comment)

My only concern with that approach is my inability to staple the cable within 12&quot; of the box - which I believe is required by NEC code 314.17(C).

Old work boxes have push-in clamps which secure the wire to the box. It's equivalent to a NM clamp on a metal box. Compare them to new work boxes sometime. Some feature that same clamp, but many merely have a break-out tab. That's where you need a staple, but since you have to attach it to a stud, your wall has to be open in some way in the first place.

Can I drill a hole in the stud right above the current j box, add an old work box on the other side of the stud, and simply feed the existing cable through the new hole into the new box?

Not really. You're going to lose 3-4&quot; off your wire doing that, meaning they won't reach the location of your new box. The only solutions here are

Gain access from above. If the wires are running just right, you can drill a hole in the top plate, pull the existing wires back, and drop them into your new box. This is unlikely but still possible.
You'll need a second old work box above the new one somewhere. Drop the existing wires in and add new wires from this box to the switch box. Nut nut the wires off and then blank plate it. Not ideal, but you avoid re-running the wires. Doing this towards the top of the wall will be less obvious.