Don't try polishing with circular motion. Polishing
will do further damage to the polycarbonate. With fine enough sandpaper (yes, sandpaper grain 3000, 5000, 7000, 10000) it is possible to cause so fine scratches that are not a problem (anymore). This is replacing few big, problematic scratches with many fine, unproblematic ones. Lastly I always use fine car polish with wax.
I've revived seemingly hopeless CDs/DVDs that looked like
with that method. When applying 3000 grain sandpaper the disc becomes completely non-reflective. Gives the feeling:
"Oh no!! Now I've ruined it!" It becomes shiny again when using finer grain and the wax at the end.
Why not in circular motion? Because any scratch, even a fine one, that follows the spiral track might make one or two complete sectors fully unreadable (while not hitting any other sectors). Scratches in random directions will hit many sectors, but only a bit, so the error correction has a good chance to recover.
Disc resurfacing can be found on YouTube, there are some good tutorials. But this is not something one should do without practicing on garbage discs -- and it is not the first thing to try (I would say it is the last thing to try, as it carries the risk of making things much worse).
Lastly, DVDs (which GC/Wii discs are based on) are more likely to survive scratches from both sides because the data layer is in the middle. On CDs the data layer it is near the label side (on the top) and on BDs it is at the very bottom.
Yes, definitely try multiple drives. In my experience console drives (and slim laptop drives) are often garbage grade compared to full-sized PC drives. I've got a few PlayStation 2 DVDs that won't work in any PS2... but a good PC drive copied them at full speed without error (ESR patched DVD-R copies work flawlessly in PS2). For GC/Wii we run into the problem that they are not standard DVDs and not detected by normal drives (and only some old IDE-based Hitachi-LG drives can indirectly dump them through undocumented debug commands).