You should check your bit, the dogs from Rockler and others are made to fit a 3/4" hole. Some are spring loaded. In solid wood workbench tops, the wood can move. If the holes were precise, you may not get the dogs in. The holes are 1/32" larger than the dogs. Solid core doors are filled with particle board. It doesn't drill that cleanly and the holes may degrade with frequent use. Whether you decide to use a router or a drill bit, use a tight fitting backer so the exit doesn't blow out, or drill until the point just comes through and then drill from the opposite face. A trick to keep the drill straight, in addition to a guide block, is to hold it out at arms length, not in close to your body. That way you can see if it's perpendicular much easier.