Though I rarely have need for bench dogs as you know them, there are needs from time to time that could be simplified if you have them. On the Paul Sellers’ bench, filling the well area in front of the vise, I introduced a laminated wooden block made from two-by stock that can stay in place or be stowed. dead simple, totally effective and low cost. Two bucks tops.
Glue-lam 8 pieces of two-by together after surface planing the wide faces of the pieces first. The pieces should ripped to the depth of the well. Also, it’s best to plane down the narrow edge of the pieces to remove the round corners on the edge. Half the work of the wide faces.
Plane up the surfaces flat and true.
Plane the laminated block to fit between the apron upstand and the main bench top.
On one edge, the edge that butts up against the apron board upstand, plane the edge about 1/8” out of square to give block a leading edge into the well when installing.
With the block fitted, drill a 3/8” dia hole in the centre of the block and equi-distant top and bottom. Depth around 1” or so. This hole houses a dowel or a metal pin that locks into the back edge of the main bench top and stops the block from rising under clamping pressure.