Big mirrors do a lot for a space despite challenge. If the look is more contemporary, keeping the mirror is a good idea. If you built a cabinet in the middle, could you hang sconces at end walls and on the new cabinet so the face on both sides was framed by lower light? Then you can use one of those super mirror frames that you just attach to what you have - when you lose the little backsplash you will have room for it and then they will look like two large framed mirrors - you can do a little row of accent glass between frame and new counter.