Electrical – Adding a spacer block between king stud and switch box

Because it is drywall, you can do pretty much as you suggest:

• Enlarge the existing hole enough so that you can drill a hole through the stud
• Cut a hole for the switch above the light switch box
• Take the door switch off the cable and feed the cable through the stud
• Use a coathanger/hook/other tool to catch the cable and pull it through the new hole
• Reattach the switch and install into the wall
• Plaster and smooth old hole
• Paint as necessary

Job done.

As far as I know junction boxes are ok for closets. Your local jurisdiction may have other ideas. Please consider consulting them.

Today's circuit panels are full of (expensive) AFCI breakers that will be damaged by flooding and running many wires can get expensive with current copper prices. Could you instead run a heavier gauge wire to a subpanel located above the water line and nearer to the loads, and branch out from there?

Also using junctions to "split" a circuit to go two directions should be used sparingly. Most electricians will expect wiring to "daisy chain" from point to point, junctions can make fault tracing much more difficult. Some jurisdictions require that the wire be unbroken from the panel to the first load.