SCRATCH REMOVAL:
Here's how the first attempt at scratch removal went. All of my research pointed to baking soda toothpaste. The simpler, the cheaper, the better. So I bought Tom's Natural baking soda toothpaste. Not much else in it.
The first scratch, before.
Then I put a big squirt of toothpaste, smeared it all over the scratches, rubbed it in a little and left it to sit for about 5 minutes. When I wiped it all off, the scratch looked like this:
Second scratch, before:
And after:
Third scratch, before:
And after:
Conclusion: So while baking soda toothpaste isn't a miracle worker, it does work for the smallest scratches. I think if I had rubbed it in more and left it to sit for 10 minutes, instead of 5, it might have worked better. I would recommend it if your algae scraper scratched your glass just a little or if you accidentally scraped some substrate along the side of the tank. Small scratches. Teeny ones. But it works great for those!
Next complete water change I'm going to try the cerium oxide powder and buffing discs I bought online. I'll update the thread again with those results too.