Get some mtb pedals and shoes, they can be used on road bikes.
Road pedals that are made for shoes with protruding cleats won't work with shoes that have recessed cleats.
If you could get a shoe with a 3 screw cleat that's recessed, the recessed cleat wouldn't protrude enough to clip into a road pedal, if the cleat protruded enough to clip into a road pedal the shoe wouldn't be any better to walk in then a road bike shoe.