Update: success! :buffing:Im the MAN
I did have to start over, basically, and although I was trying to avoid that when I started this thread, ultimately I wanted the spots gone.
In one last ditch effort I decided to get very aggressive. I picked up some M105 at Autozone (overpriced, I know, but patience was not on my side today!) and paired it with a microfiber cutting disc, high pad rotating speed and firm pressure. M105 has not been my favorite in the past because of the dusting and how it can be tricky to use, which is why I never replaced it when I ran out of my first bottle. But when you have to break out the big guns, you gotta do what you gotta do.
I made sure to keep my working time short and my sections small, and used a bit of clay lube here and there. I was pleasantly surprised by the finish I was getting with M105. It wasn't half bad!
What water spots?
I dig this color. Copper Red, Mazda calls it. The gold flake adds so much when the paint is clarified enough that you can see it.
After this I put a couple of polishes up against each other to decide what to use on the rest of the car. I had my trusty inexpensive Meguiars Ultimate Polish around, which I knew would give solid results. The challenger was Pinnacle Advanced Finishing Polish. I was so impressed by my friend's Pinnacle's Advanced Swirl Remover the first time I detailed this car, I had to buy some of my own and I added their polish to my cart, because why not [raise your hand if you suffer the same affliction!].
On the left we have Pinnacle AFP. The middle is the tape line which shows how M105 finished on its own. The right is Meguiars UP. This shows that even if M105 looks good in isolation, there's definitely more clarity on offer with a finishing polish.
[ Edit: Pinnacle AFP was applied with a black foam finishing pad, and Meguiars UP was applied with a yellow polishing pad. ]
I can't tell any difference between the polishes, even with the naked eye (which is far better than my photography skills

). I was a little surprised at this given one has some fillers and one does not.
I'll be using the Meguiars UP on the rest of the car when I get back to it tomorrow. I'll keep Pinnacle AFP around for other opportunities. Given the price difference, unless I see AFP stand out on other cars I test with, I'll be sticking with Meguiars UP and M205 to satisfy my cheapskate side.
Thanks again for all the help folks!