first things first as mentioned above above cutting the whole sill of, i say dont, never cut off more metal than you need to
i would butt weld that you shouldnt need another strip of steel inside unless you dont trust your welding. i would zinc spray the inside of the sill first and the inside of the part you are welding in, then waxoil inside the sill when finished
i wouldnt do a lap joint on any part of a car i can not get to both sides of to seal afterwards as lap joints are notorious for being moisture traps