Hello again James.
Great looking bench and vise. In the past I have just chiseled (or I hate to admit it, routed) out a recess in the underside and tail end or face of the bench top to accept it but just be sure to keep all of the metal below the top. If it is a little below the bench top it won’t matter much as long as the dog is long enough. You can drill depth controlled holes in the recess area to help keep the chiseling at a controlled depth if necessary. That would normally best be done with the top removed and turned over on the base. I normally line the jaw faces with wood with the back jaw liner flush with the end or front edge of the top, and thin leather to pad the jaw liners and help them hold the work pieces and to prevent damage to the work pieces. The wood liners could be placed just above the bench top and planned down to match it after installation. I have a second bench that is used primarily for working on tools and general rough work. That set of vices are just wood lined and sit proud of the bench edge. I also have some metal working vises and I have them mounted on ply and just clamp them to the bench top when I need them.
My bench dog holes were based on dogs that I had, are 3/4 inch in diameter and can be used with my hold fasts. There is an old saying: buy (or make)your hardware and design the features (in this case holes) around that. I have seen dogs and hold fasts sized for 3/4 and 1 inch holes as well as dogs for square holes.