I don't know of any cleat/pedal/shoe system that will let you put your cleat as far back as you require. If you are willing to sacrifice a pair of shoes, you might try drilling new cleat mounting holes in the shoe's instep and recessing the inside mounting plate as far as possible to avoid having it bother your arch. A padded insole may be needed too.

Shimano SPD's or Wellgo's knock-offs are probably the smallest cleats available and would allow the furthest rear placement. Look, Time and similar systems, with their large cleats, seem like a poor bet.