Moving House Electrical Outlet
As the good commenters mentioned you cannot bury the junction box, it must remain accessible.  A hinged bench seat sounds like a great workaround.  That space under the bench could be considered part of habitable space though, so the cable would need to be protected in a raceway or conduit.  It would be acceptable to build a short raceway out of 2x4s.
But if you're going to have a hinged bench anyway, would it be so bad to just leave the receptacles as-is, and when you need them open the bench?  You could leave a little notch in the back of the bench so you could close it after plugging in the vacuum or whatever you'll be plugging in. Or run a power strip out of it.
[EDIT: A cable coming out the blue box and into the void behind the wall could route into a raceway that terminates into the same wall void, adjacent to the blank cover.  The reason you cannot have a cable run out of a hole in the blank cover itself is that would be unprotected.  Protecting that cable coming out the coverplate makes the junction box inaccessible.  What you could do instead is use an extension box that you could screw conduit into:   The box extension comes with some plugs to plug one of the holes, and the other hole would be your plastic or metal threaded conduit terminal adapter (must connected ground to it if its metal).]