On completion, you will graduate with a set of self-made tools, fixtures and storage units (not to mention the skills required to build them) that will serve and last you the rest of your life. You’ll be amply prepared to continue your woodworking education into specific trades such as architectural woodworking (finish work); custom door and window construction; solid-wood furniture and cabinetry; and boatbuilding. Over the course, we invite guest lecturers from the community to share their experience of becoming vocational woodworkers in these trades.
A better solution would have been to route a rabbet into the side, so that the added strip always had thickness. The way I did it means that the strip I glued in is very narrow, and hence very weak, at a certain point. In this case, that's not a problem, because it's going to be sitting under the countertop layer. I also noticed that because I had only clamped the strip down, and not into the edge, there was a noticeable glue gap where the strip butted up against the MDF. Again, in this application it isn't visible. But if I was doing something like this on the top of a table, I'd make sure to cut a clean rabbet, and to clamp both down and in.
So drill the benchdog holes through the MDF layer. Begin by laying out their positions. You'll want these to be precise, so that the distances between the holes are consistent. The vises you are using will constrain your benchdog spacing. My front vise worked most naturally with two rows of holes four inches apart, my end vise with two pairs of rows, with four inches between the rows and eight inches between the pairs. Because of this, I decided on a 4" by 4" pattern.