@Scott ***********
More or less your conclusion is correct.
Only a few exceptions. When your first report is early, maybe because day 90 and up are inconvenient for you to visit Immigration, your second need to be done before day 180, because the counter starts again the moment you did report.
The other exception is when you extend in country.
But even when you need to report in person, you can just try to report online, it is easy and free and when you got rejected you can print the filled in PDF to report in person.
Sometimes they just accept, like my latest report.