I'd use the blank cover with the knockout and a 90 degree FMCMC connector (shown below) and run the FMCMC stapling it to the edge around the storage bench. Then terminate it in a metal old work box. Connect the ground from you FMCMC to the ground in the old outlet box, either a grounded metal box or NM cable ground. At you new outlet box, connect your ground wire to the metal box with 10-32 grounding screw.
Check your breaker size to determine the wire size you can run: 20 amp breaker- #12AWG, 15 amp breaker - #14AWG.
You might luck out and be able to get a short piece 8' of FMCMC commonly known as a whip that comes with the wire and maybe connectors.