Of course, after I go through the trouble to finally post this, I fixed it. The icon in ProgramData (#4 from above) was wrong, so I decided to delete it to see what would happen. I opened a PDF file and the icon changed to a PDF icon, not the Acrobat icon, which was progress, but still not quite right. I right clicked on the PDF icon in the taskbar, enabled pin to Taskbar for Acrobat, and then the icon was finally correct. Hopefully this helps someone.