The second discovery is Rock-On Screws. These are sold to attach cement board to studs. They countersink themselves in MDF because the underside of the heads are ridged to cut away the material under the head. They self-drill so with a little caution you can really minimize splitting MDF when running screws into the edge. They're a little expensive, but I've driven close to 500 of them and never broke one. I've broken about 5 philips bits (good ones too, DeWalt), but I never sheared off a screw head. They're a world better than ordinary sheet rock screws of any variety.