Salt steaks well on all sides and let sit at room temperature 30 minutes to an hour.
Meanwhile, preheat oven to 350°. Heat a grill to high (600° to 650°). If using a charcoal grill, prepare a bed of coals on half of firegrate (3 1/2 to 4 in. thick, from 1 heaping chimney of ash-covered coals; Alfred's uses mesquite hardwood coals); leave rest of grate clear. Set cooking grate in place. Heat it at least 5 minutes, covered, with lid and bottom vents open. If using gas, preheat grill with all burners on high 20 minutes.
Blot steaks dry and rub with canola oil. Put on a rimmed baking pan. Set a wire rack in a second baking pan and take both pans out to the grill, along with long grilling tongs.
Grilling 1 or 2 steaks at a time, sear over direct heat just until meat releases from grate, about 30 seconds. Turn and grill 30 seconds, then keep turning and grilling in 30-second bursts, including on bone side, until all sides are evenly browned, 4 to 5 minutes total. If fire flares up, move steaks to a cooler area for a moment. Lay steaks on rack in baking pan as they're done, then take inside. Keep grills going (close top and bottom vents halfway on charcoal grill to preserve heat).
Slide steaks into the 350° oven. Roast until an instant-read thermometer registers 120°, about 25 minutes for porterhouse, 20 minutes for rib-eye, and 10 to 12 minutes for filet mignon.
To finish steaks, grill over high heat on all sides, turning every 30 seconds or so, until crusty and deeply browned and porterhouse registers 125° in center for medium-rare, about 5 minutes (it will keep cooking off the heat). Grill rib-eye and tenderloins to 125° to 130°, about 5 minutes. Lift to a large cutting board as done.
Let steaks rest 10 minutes. Cut filet mignons thickly crosswise. Slice porterhouse and rib-eye from bones, then cut meat thickly crosswise and reassemble with bone. Drizzle steaks with olive oil and sprinkle with sea salt. Serve with horseradish sauce and/or béarnaise sauce.