One you have the vise jaws shaped so that the vise moves freely, mark and drill holes in the fixed jaw for the bolts that will hold it to the bench. With these drilled, reassemble the vise and mark the location of the holes with an awl. Disassemble the vise and drill the holes through the stretcher, then reassemble the vise and bolt the inner jaw in place.
Put the upper panel of MDF on your glue-up surface, bottom side up. Put the bottom panel of MDF on your other surface, bottom side down. (The panel with the holes drilled in it is the bottom panel, and the side that has the your layout diagram on it is the bottom side.) Chuck up in your drill the appropriate driver bit for the screws your using. Make sure you have a freshly-charged battery, and crank the speed down and the torque way down. You don't want to over-tighten the screws, MDF strips easily.
Assemble the vises, for the final time. You'll not be taking them off again, so tighten everything down, and attach the endplate to the ends of the screw and guide rods. Then mark and drill benchdog holes in the outer jaws inline with the benchdog holes in the top. Generally, through-holes are preferred for benchdogs, so that they don't collect sawdust and gunk. With these vises, that isn't possible, there are screws and guide rods in the way. I drilled them just deep enough to hold a Veritas Bench Pony (their reduced-height benchdog), without it sinking to where I can't get a grip to remove it. Rockler sells some very inexpensive plastic benchdogs that can't be adjusted for height, and aren't as strong as metal or wooden dogs, that I intend to keep in the holes full-time, to keep sawdust from collecting in them.
When the top is done, we want the edged MDF and the oak countertop to have exactly the same dimensions, and for their width to exactly match the width of the base.I could see three ways of doing this: 1, join the MDF to the countertop and use my belt sander to sand down their joined edges to match the base; 2, join the MDF to the countertop and use a hand plane to plane down their joined edges to match the base; or 3, use a flush-trim bit against a straight edge to route the MDF to the width of the base, then join the MDF to the countertop and use the flush-trim bit to route the countertop to match the MDF.
I used the factory edge of the half-panel of hardboard as a guide for cutting the ply. I wanted to cut a 5-1/2" strip, and my saw cuts 4-1/2" from the edge of the shoe, so I wanted the edge of the hardboard 10" from the edge of the ply. So I set my combination square to 10", and used it to mechanically set the distance. Hint - if you need two things to be precisely the same length, try to avoid measuring them separately. Use some mechanical mechanism for setting the distance.
The book is well written and easy to read. The illustrations, I'm sure were excellent in 1914 and, are still adequite now. Most of the designs seemed repetitive, though. I wish more attention had been given to lashing materials. If you are looking for that you will find almost none here. The book was fun to read and provided enough inspiration to make my brother and me attempt a large hut.