The "cookie cutter" method simply means cutting individual pieces out of a larger sheet using a jigsaw. In years past, one could either build a layout atop a continuous sheet of plywood, or cut out the plywood and place it only in areas where the track goes. What wasn't covered by plywood was an open frame covered by plaster scenery.
You are right, masonite is hard stuff. I either beveled the edges using a router or a sander after the individual shapes were cut from the larger board. I either glued the roadbed to the plywood underlayment with yellow glue, or fastened it using small nails. In those days, I used atlas code 100 track, and I simply drove the atlas track nail through the hole in the tie and into the masonite. If I was doing it again, I would glue the track down using latex caulk.
Kevin