David Barnett
"Fill in the gaps for me - we're now, in essence, machining our own surface plates in order to act as a backer for lapping with diamond paste, right? Is that what all of this is about?"

Yes. And no.

We're a long way from making a surface plate, which generally requires a much flatter surface than a lap referenced off of a surface plate.

Iron surface plates have stability issues that require careful design, casting and fabrication, quality control, controlled seasoning of the iron (webbed or solid), calibration and maintenence to flatness and surface standards, often requiring optical flats. You wouldn't charge the surface of your iron surface plate with diamond grit unless you didn't want it for a surface plate any longer.

No, we're just flattening a piece of cast gray iron into a lap; something flat to hold diamond really well, using a surface plate or other flat reference surface to expose the distribution of high points as we refine the lap surface. Once done, it can be used to further flatten plane blade and chisel backs with a coarser grit of diamond or other hard, blocky abrasive, or more for our everyday sharpening purposes, charged with fine diamond grit to quickly hone plane blade and chisel edges to an acceptable degree of sharpness.

Our reason to scrape iron, whether repurposed, scrap, or commercial stock, is mainly to, for whatever reason, not engage a machinist with a surface grinder to do that work for us. Also, scraping has other uses around the woodworker's shop, such as flattening iron plane soles, improving the fit of frog to plane body, and occasionally to true or restore ways, tables and fences on woodworking machines. And if you find it enjoyable, you can make really flat, accurate straightedges, too.

It's not for everyone, obviously, but adds another skill to our toolkit, is terribly cheap, especially if you make your scraper from an old file and have a tube of oil paint or even lipstick lying about, and means you don't have to go outside your shop to a machinist to do things for you.

Bill Tindall has done that very thing; engaged a machine shop and is very satisfied with his results. This is the fastest, most direct way to get your plate flat. Even so, I'm apt to scrape what comes from the surface grinder, but that's just me. Some have had less satisfactory experiences with machine shops. One highly skilled woodworking teacher had plane soles and sides ground unacceptably thin. Sometimes it's hard to get a machine shop to bother with woodworking tools for a reasonable price, or at all, for that matter. So under these circumstances, scraping is a viable workaround.

You may not realize that lapping plates have been used for sharpening woodworking hand tools for years, not a new thing ("we're now"). Harris made a lapping kit for woodworkers that gained a following a couple decades back. I encountered it during my first woodworking school experience and loved how fast a blade got flat with SiC and sharp with diamond paste. With the advent of truly cheap industrial diamond, lapping has become more popular for putting that final edge on a blade, handling the toughest, hardest tool steels with ease.

By the way, one woodworker/designer who studied under Tage Frid and Seth Stem at RISD swore by the Harris System. No, not Frid's style. It's my understanding that Frid was far more focused on instilling pragmatic business survival practices in his students than fussing about details as to how one got something done. You got it done. Period.

So, to answer your original question, no, we're not making surface plates, won't be using our laps as reference surfaces other than to flatten a blade face (or back) and get a good edge. We're making iron laps as an optimal substrate for diamond sharpening. Cheap, doesn't take long, is kind of fun, and works really well.