Bram,
I would not try to sand out the scratches as a first step. The cast is rather soft, and I would use a smoothing file as a first step, probably an 8 inch or 6 inch. I would lay the file dead flat on the plane and file over the scratches first. The file will take off the high part of the scratches that are proud of the surface of the sole of the plane extremely rapidly. That step will be very easy and very quick. Drastically less time than your float glass and sand paper. I would say it could be done in a couple of minutes or so. Be sure to use a light touch, as a new sharp file should cut high spots along the edges of the scratches on the old cast iron sole in literally a few swipes. The file will likely leave some scratches of it's own, but they will be very shallow. The next steps, below will take care of remaining burrs, sharp edges of the deep scratches and some of the tiny scratches from the file.
Once you have the high raised edges of the scratches gone then I would use your float glass and sandpaper. I would use moderately fine sandpaper first, probably 220, followed by 320. You should not have to us the sand paper very long, maybe a few minutes at the very most with each grit, the idea being to use the file to quickly remove the edges along the scratches that the tip of the screw made.
I certainly would not to work the sole down until the scratches were gone, there is no need and no advantage to such. All you really need to do is get the sole to the point that the edge of the scratches are back down level with the rest of the sole. I might then rub it down with some of the red/brown Scotch Brite pad to remove the sharp edges and any burrs that remain. You just need to get it to the point that it won't catch any wood fibers or scratch the wood you are planing. The Scotch Brite pad is to round over the sharp edges of the scratches once you have removed the edges that protrude above the surface of the metal with the file and fine sandpaper. Thus getting the scratches flat with the surface again.
You had that plane working very well before the scratches happened. It will take very little to take care of the scratches and to get it back to the point that it again works very well.
That said, if you decide to buy one of the other planes, like Jim, I would by the second plane in a heartbeat. It is an older stanley, and they were better, and much more carefully, made than the newer Stanley planes like the first one shown. That said, check the older Stanley out well before you buy it. Make sure it has a flat sole, etc.
Regards,
Stew