You are right. You do have a mess.
I suggest putting the compound away and start working patiently on each section with a polish -- almost any polish -- following Mike's suggestions. I guess the latest and greatest polish would be Meguiar's 205.
This is a job that I most certainly would not like to tackle by hand. You may want to have a pro buff it out for you. Then you can go into a maintenance mode.
Tom

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